Parallel processing for solution space partitions

ABSTRACT

Systems, devices, methods, and computer-readable media are disclosed for utilizing group theoretic techniques to enable data exchange between a supervisory central processing unit (CPU) and a group of graphical processing units (GPUs). The CPU may be configured to utilize a tabu search metaheuristic to explore a solution space to determine an optimal solution to an optimization problem. More specifically, the CPU may determine a fragmentation of a solution space that yields multiple partitions of the solution space and may assign each partition to a respective GPU configured to calculate a computational result. The CPU may then determine a new fragmentation of the solution space based on the computational results received from the GPUs that yields new partitions of the solution space and may assign each new partition to a respective GPU configured to again generate a computational result based on its assigned new partition. The CPU may continue to determine new fragmentations based on the computational results of the GPUs until stopping criteria are satisfied and a timely, high-quality solution to the optimization problem is determined.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to, the benefit of, and is a divisionalapplication of U.S. application Ser. No. 15/154,392, filed May 13, 2016,which claims priority to U.S. Provisional Application No. 62/162,069,filed May 15, 2015, and U.S. Provisional Application No. 62/237,425,filed Oct. 5, 2015, which are all hereby incorporated by referenceherein in their entirety.

BACKGROUND

Solving an optimization problem involves finding an optimal solutionfrom a set of candidate solutions. Optimization problems includeminimization problems in which the optimal solution is a solution thatminimizes an objective function subject to one or more constraints ormaximization problems in which the optimal solution is a solution thatmaximizes an objective function subject to one or more constraints.Optimization problems may involve discrete variables and/or continuousvariables. An example of an optimization problem involving discretevariables is a combinatorial optimization problem for which an optimalsolution may be a discrete element (e.g., an integer, permutation,graph, etc.) from a finite (or possibly countable infinite) set. Anoptimal solution to an optimization problem that involves continuousvariables may include a sequence of values for each of the continuousvariables.

BRIEF DESCRIPTION OF DRAWINGS

The detailed description is set forth with reference to the accompanyingdrawings. The drawings are provided for purposes of illustration onlyand merely depict example embodiments of the disclosure. The drawingsare provided to facilitate understanding of the disclosure and shall notbe deemed to limit the breadth, scope, or applicability of thedisclosure. In the drawings, the left-most digit(s) of a referencenumeral identifies the drawing in which the reference numeral firstappears. The use of the same reference numerals indicates similar, butnot necessarily, the same or identical components. However, differentreference numerals may be used to identify similar components as well.Various embodiments may utilize elements or components other than thoseillustrated in the drawings, and some elements and/or components may notbe present in various embodiments. The use of singular terminology todescribe a component or element may, depending on the context, encompassa plural number of such components or elements and vice versa.

FIG. 1 depicts an example system architecture including a supervisorycentral processing unit (CPU) and a multi-core graphical processing unit(GPU) containing multiple GPU threads, where each GPU thread isconfigured to process a respective fragmented portion of a solutionspace in accordance with one or more example embodiments of thedisclosure.

FIG. 2 depicts an example hardware architecture of a supervisory CPU andan example hardware architecture of a GPU in accordance with one or moreexample embodiments of the disclosure.

FIG. 3 depicts an example configuration of a streaming multiprocessor ofa GPU in accordance with one or more example embodiments of thedisclosure.

FIG. 4 depicts an example configuration of a thread processing clusterof a GPU in accordance with one or more example embodiments of thedisclosure.

FIG. 5 depicts an example configuration of a GPU in accordance with oneor more example embodiments of the disclosure.

FIG. 6 is a process flow diagram of an illustrative method for executinggroup theoretic tabu search (GTTS) processing to determine a finalsolution to a program representative of an optimization problem inaccordance with one or more example embodiments of the disclosure.

FIG. 7 is a process flow diagram of an illustrative method forfragmenting a solution space into a plurality of cells, fragmenting eachcell into a plurality of sub-cells, and providing each sub-cell to arespective GPU for executing GTTS processing on each sub-cell inaccordance with one or more example embodiments of the disclosure.

FIG. 8 depicts an example system environment for multiple carrierdispatch optimization, according to one embodiment of the disclosure.

FIG. 9 is a process flow diagram of an illustrative method for optimallyassigning a vehicle to a carrier for dispatch, according to oneembodiment of the disclosure.

FIG. 10 is an example process flow diagram of an illustrative method forselecting an optimal vehicle shipment route, according to one embodimentof the disclosure.

FIG. 11 is a flow diagram illustrating of an illustrative method foroptimizing one or more carrier routes for picking up and/or deliveringmultiple vehicles, according to one embodiment of the disclosure.

FIG. 12 is a schematic block diagram of an illustrative serverconfigured to execute GTTS processing in accordance with one or moreexample embodiments of the disclosure.

DETAILED DESCRIPTION Overview

This disclosure relates to, among other things, systems, devices,methods, and computer-readable media for utilizing group theoretictechniques to enable data exchange between a supervisory centralprocessing unit (CPU) and a collection of graphical processing units(GPUs). In certain example embodiments, the CPU may be configured toutilize a tabu search metaheuristic to explore a solution space todetermine a timely, high-quality solution to an optimization problem.More specifically, the CPU may determine a fragmentation of a solutionspace that yields multiple fragments (also referred to herein aspartitions) and may assign each partition to a respective GPU threadconfigured to calculate a computational result. The CPU may thendetermine a new fragmentation of the solution space based on thecomputational results received from the GPU threads that yields newpartitions of the solution space and may assign each new partition to arespective GPU thread configured to again generate a computationalresult based on its assigned new partition. The CPU may continue todetermine new fragmentations based on the computational results of theGPU threads until stopping criteria are satisfied and a timely,high-quality solution to the optimization problem is determined. Incertain example embodiments, the stopping criteria may be a thresholdnumber of iterations (e.g., a threshold number of new fragmentations)during which an improved solution to the optimization problem is notfound. The timely, high-quality solution to the optimization problem maythen be the best solution determined up until the stopping criteria aresatisfied. The best solution may be the solution that most optimizes(e.g., most minimizes or most maximizes one or more variables) among allsolutions determined up until the stopping criteria are satisfied.

Particular embodiments of the subject matter described herein can beimplemented so as to realize one or more of the following improvements.Provide accurate and efficient methods for optimizing delivery routesutilizing parallel processing of one or more specialized processingunits. In turn, this increases the speed of optimization and reduces thecomputational stress on servers and components responsible for theoptimizations. Ensure faster deliveries and in turn improves the userexperience; and reduces the cost associated with deliveries and mayincrease revenue.

An example optimization problem capable of being solved using, forexample, GTTS processing in accordance with example embodiments of thedisclosure may be an n-city, m-Traveling Salesman Problem (TSP). Atimely, high-quality solution to an n-city, m-TSP optimization problemmay be one that identifies the most profitable routes (e.g., lowesttotal distance traveled) for a fleet of agents to travel to pick up anddrop off items (e.g., vehicles) during specified time windows. Morespecifically, in an n-city, m-TSP optimization problem, m agents may berequired to visit n locations (e.g., cities) to pickup/deliver vehicles.Vehicle pickups and deliveries may occur during specified time windows,with each city being visited once by only one agent, and each agenthaving its assigned collection of cities. In addition, each agent may berequired to return to the city from which it initially started itsroute. A solution to the n-city, m-TSP optimization problem may identifywhich cities (and in what order) are visited by which agents.

For n cities and directed distance d_(ij) from City i to City j,intercity distances may be represented in a 0-diagonal n×n matrix D ofnon-negative real numbers. Although D is typically symmetric, D may alsobe asymmetric, in which case, the directed distance d_(ij) from City ito City j may differ from the directed distance d_(ji) from City j toCity I for one or more pairs of cities i,j. Each agent may be associatedwith a subtour which may represent the order in which the agent visitsits assigned cities. The subtours for all agents may collectivelycomprise a tour. The set of all tours may be represented as the elementsof S_(n), the symmetric group on n symbols. Each element represents abijective function from the set of n symbols onto itself, and the groupoperation (permutation multiplication) is function composition. Thesubtours of a tour may be the disjoint cyclic factors (DCFs) of thepermutation that represents the tour.

For example, if two agents visit cities 1 through 7, then the tourrepresented by the permutation p=(1, 5) (2, 6, 3, 7, 4)∈S₇ includessubtours represented by the disjoint cyclic factors (1, 5) and (2, 6, 3,7, 4). In this example, a first agent may visit cities 1 and 5, while asecond agent may visit the remaining cities, with each agent returningto the city from which it started. Further, a cycle's tourlength may bethe sum of each of its arclengths, and a tour's length may be the sum ofthe tourlengths of the subtours that comprise the tour. For example, forthe tour represented by the permutation p=(1, 5) (2, 6, 3, 7, 4), thetour's length may be the sum of the tourlength of the subtourrepresented by the DCF (1, 5) and the tourlength of the subtourrepresented by the DCF (2, 6, 3, 7, 4). The tourlength of the subtourrepresented by the DCF (1, 5) may be the sum of the arclengths betweencity 1 and city 5 (e.g., the directed distance from city 1 to city 5)and between city 5 and city 1. Further, the tourlength of the subtourrepresented by the DCF (2, 6, 3, 7, 4) may be the sum of the arclengths2→6); (6→3); (3→7); (7→4); and (4→2).

In certain example embodiments, group theoretic approaches may be usedto generalize the n-city, 1-TSP problem using the equation p*W, wherep=the permutation composition of k cyclized subpaths (e.g., the DCFs ofp) and W=set of full cycles on T U complement (mov(p)), where T is theset of subpath tails of p, * is permutation composition, and mov(p) isthe set of symbols in the DCFs of p. The use of the above-describedequation p*W for solving a n-city, 1-TSP optimization problem allowsdiverse tours to be created that preserve properties associated withdesirable solutions.

More generally, an optimization problem such as the n-city, m-TSPproblem may be represented as a mathematical program (MP). An MP is asystem of equations in which one or more objective functions areoptimized over a region defined by one or more constraint equations.Various types of methods may be used to solve an MP. Exact methods aredesigned to determine global optima to an MP. Exact methods, however,may fail to determine global optima within a time constraint associatedwith application of the MP. Heuristic methods may also be used to solvean MP. Heuristic methods utilize deterministic and probabilistic methods(e.g., quasi-random number generation) to attempt to obtain ahigh-quality solution to an MP within a time constraint. Heuristicmethods, however, may fail to obtain such a high-quality solution sincethey utilize empirical results that cannot guarantee high-qualitysolutions. Yet another example of a type of method that may be used tosolve an MP is a metaheuristic method. A metaheuristic method utilizesheuristics to manage the use of heuristics. Tabu search, neuralnetworks, and genetic algorithms are examples of metaheuristic methods.Group theory is a branch of mathematics directed to the properties ofgroups, a type of algebraic structure. Example embodiments of thedisclosure utilize group theoretic techniques to implement tabu searchusing multiple GPU threads configured to perform, for example, GTTSprocessing on respective partitions of a solution space in parallel. Inone implementation, GTTS processing may be used by GPUs to search theirrespective assigned solution space portions. However, other suitableprocessing methodology may also be used, either alone or in combinationwith GTTS. In one example, simulated annealing may be used by GPUs tosearch their respective assigned solution space portions. Similarly, agenetic algorithm may be used by GPUs to search their respectiveassigned solution space portions. It should be understood that the abovesearch and processing methodologies are example processing methodologiesand are not to be construed as limiting.

An MP may take on various forms. For example, a linear program (LP)expressed in matrix form optimizes c^(T)x for Ax=b and x≥0, where b, cand x are column matrices and A is an n-row rectangular matrix A havingrank n. All matrix entries are real numbers and all entries are knownconstants except for those of x. A network program is an LP whoseA-matrix is totally unimodular. A goal program is an LP with multiplelinear objective functions. A goal program minimizes the summed absolutedifferences of each objective function from its user-specified targetvalue.

An integer program is an LP as defined above with the additionalconstraint that x is an integer vector. When suitable constraints areadded, an integer program can be solved as an LP. The group minimizationproblem converts an integer program into a 1-constraint MP whosevariables are clock group elements. This transformation arises when theSmith Normal Form of the optimal basis matrix (of the relaxed LP model)has a lone nonzero element greater than 1. A mixed integer program is anLP having continuous and integer variables. A nonlinear program is an MPthat has a nonlinear objective function or constraint. A convex programis an MP whose feasible region is a convex set. Each of theabove-described MPs includes no random variable. A stochastic program,on the other hand, is an MP that includes random variables. A dynamicprogram is a multistage MP (with or without random variables) that lacksa structured form. Each stage of a multistage MP is in one of a finitenumber of states, and the current state affects the choice of the nextstage's state. Given the current state, an optimal policy for theremaining stages is unaffected by earlier choices.

Optimization problems capable of being solved using, for example, GTTSprocessing in accordance with example embodiments of the disclosureinclude, for example, MPs that include continuous variables, MPs thatinclude discrete variables, and MPs that include discrete and continuousvariables (also referred to as mixed MPs). Examples of such MPs includeinteger and linear programs. More specifically, example embodiments ofthe disclosure may utilize GTTS processing to solve MPs having thefollowing form: optimize g₁(x), . . . , g_(n)(x) for x∈S ⊆Ω, where S(the feasible region) is a subset of set Ω (the universe). In turn, theset difference Ω−S is the infeasible region. S may be a set of variables(discrete, continuous, or mixed), and, in certain example embodiments,may be a Cartesian product of other sets, in which case, x may bemultivariate. Solving such an optimization problem involves eitherdetermining any optimum x or determining all such optima. For instance,an integer program may have a relatively small collection of optimawhereas a linear program's optimal solution space may be the convexcombination of all optimal vertices on the polyhedron S. The g_(k) arethe objective functions whose manner of optimization is user-defined,e.g., find all joint optima x; optimize g_(k+1) over the optima obtainedfor g_(k); or minimize the summed absolute differences of each objectivefunction from its user-specified target value. Optima may be obtainedvia exact methods if capable of being achieved within a time constraint.Alternatively, heuristics may be used that, in turn, may apply exactmethods to tractable smaller problems.

Example System Operation and Processing

FIG. 1 depicts an example system architecture including a supervisorycentral processing unit (CPU) 102 and a multi-core graphical processingunit (GPU) 104 containing multiple GPU threads, where each GPU thread isconfigured to process a respective fragmented portion of a solutionspace in accordance with one or more example embodiments of thedisclosure. It should be appreciated that FIG. 1 depicts an exampleconfiguration of the supervisory CPU 102 and the multi-core GPU 104 andthat other configurations including additional and/or alternativehardware, firmware, and/or software components are also within the scopeof this disclosure.

The supervisory CPU 102 may include a pre-processor 108 configured toreceive input data and constraints 106 as input. The input data 106 mayinclude data relating to an optimization problem to be solved such as,for example, the n-city, m-TSP problem. For example, the input data mayindicate a number of cities, inter-city distances between each pair ofcities, and a number of agents designated to travel between the cities.In the case of the n-city, m-TSP problem, the constraints 106 mayinclude an identification of which cities much be visited by a specificagent, an order in which cities must be visited, and so forth.

The pre-processor 108 may be configured to select an appropriate MP forrepresenting the optimization problem based at least in part on theinput data/constraints 106. For example, the pre-processor 108 maychoose a particular type of MP to represent the optimization problemamong candidate types of MPs. The candidate types of MPs may include alinear program, an integer program, a mixed integer program, a nonlinearprogram, a convex program, a stochastic program, a dynamic program, orthe like. For example, the pre-processor 108 may select an integerprogram to represent the n-city, m-TSP problem.

Upon selection of a type of MP to represent the optimization program tobe solved, the pre-processor 108 may communicate an identification ofthe selected type of MP to a master program module 112. Thepre-processor 108 may further communicate a set of initial variables tothe master program module 112. The master program module 112 may beconfigured to determine a solution method to use to solve the selectedtype of program. For example, the master program module 112 maydetermine whether to utilize an exact method or a tabu search method tosolve the selected type of MP. Example embodiments of the disclosure inwhich the optimization problem to be solved is the n-city, m-TSPoptimization problem assume that the master program module 112 selects atabu search method to solve the optimization problem. Accordingly, insuch example embodiments, the master program module 112 may initialize aGTTS program module 114 to perform GTTS processing to determine one ormore solutions to the problem represented by the selected type of MPfrom within a solution space and within a specified time constraint. Amost elite solution (e.g., a solution that most minimizes or maximizesthe one or more objective functions of the optimization problem amongthe determined solutions) may be a globally optimal solution but may notbe confirmable as such.

The GTTS module 114 may determine an initial solution to the selectedtype of MP that is representative of the optimization problem to besolved. In certain example embodiments, the initial solution may be anelite solution that satisfies stopping/halting criteria for halting theGTTS processing. For example, in the case of the n-city, m-TSPoptimization problem, the initial solution may be a permutationrepresentative of a tour between the n cities, where the permutationcontains one or more DCFs, each DCF being representative of a subtourbetween a disjoint subset of the n cities. In other example embodiments,the initial solution may not be an elite solution that satisfies thehalting criteria, in which case, the GTTS module 114 may determine aninitial fragmentation of the solution space. The GTTS module 114 may beoperatively coupled to a host memory 122. The GTTS module 114 may launch124 a respective kernel corresponding to each solution space partitiongenerated as a result of the fragmentation of the solution space. Thekernels may be launched by the CPU 102 on a device memory 126 of themulti-core GPU 104. Each kernel may be associated with a correspondingGPU thread in a collection of GPU threads 128(1)-128(N) contained in themulti-core GPU 104. More specifically, each kernel may manage theprocessing of a corresponding solution space fragment that is performedby a corresponding GPU thread of the collection of GPU threads128(1)-128(N).

Each GPU thread may generate one or more computational results (e.g.,one or more elite solutions) as a result of processing performed on acorresponding solution space fragment. The device memory 126 may thenprovide the computational results 130 from the GPU threads 128(1)-128(N)to the host memory 122. The GTTS module 114 may then determine anupdated fragmentation of the solution space based at least in part onthe computational results 130. The host memory 122 may then communicatethe new solution space partitions obtained from the new fragmentation tothe device memory 126, which may in turn, assign a respective newsolution space partition to each GPU thread in the collection of GPUthreads 128(1)-128(N). Each GPU thread may explore its corresponding newsolution space partition and generate one or more computational results(e.g., one or more elite solutions), which may be provided by the devicememory 126 to the host memory 122. The GTTS module 114 may determineadditional fragmentations of the solution space, which may be processedin parallel iteratively by the collection of GPU threads 128(1)-128(N)until halting criteria are satisfied and an elite solution is chosen asa timely, high-quality solution to the optimization problem. In certainexample embodiments, the halting criteria may be a time constraintassociated with the optimization problem. For example, after apredetermined time period has elapsed, a most optimal elite solutionobtained to that point may be selected as a final solution to theoptimization problem. In other example embodiments, the halting criteriamay be additionally or alternatively defined by a threshold number ofiterations of the GTTS processing (e.g., a threshold number offragmentations of the solution space).

In certain example embodiments, at least a portion 118 of thecomputational results generated by the collection of GPU threads128(1)-128(N) may be communicated by the GTTS module 114 to the masterprogram module 112. The master program module 112 may store thecomputational results 118 in one or more archival datastore(s) 120. Thecomputational results 118 stored in the datastore(s) 120 may be used todetermine an elite solution to select as a new initial solution for theGTTS processing when GTTS processing performed on a previously selectedinitial solution fails to generate any additional elite solution(s). Inaddition, the computational results 118 stored in the datastore(s) 120may be used to ensure that GTTS processing performed with respect to acurrent elite solution does not cycle back to an existing elite solutionthat has already been processed.

Referring in more detail to the fragmentation performed by the GTTSprogram module 114, the fragmentation may split the solution space Ω(e.g., the group of all permutations of a set M which, in turn, is thesymmetric group of the set M) into disjoint subsets referred to hereinas cells. The GTTS processing performed by the collection of GPU threads128(1)-128(N) may not be able to fully explore any given cell since thecell size (e.g., the number of permutations in the disjoint subsetcorresponding to the cell) may be large. In certain example embodiments,an initial solution to the optimization problem may be chosen and theGTTS processing may be initiated in the cell that contains the initialsolution. When the GTTS processing fails to identify any new elitesolution within the current cell, the GTTS processing may continue bydiversifying the exploration of the solution space and continuingprocessing in another cell. As such, cells may also be referred toherein as diversification cells.

As previously described, an initial solution may determine the initialfragmentation of Ω. That is, negative entries in the matrix ^(p)D(described in more detail hereinafter) may identify the arcs among whichis one that yields a better solution than the initial solution. This useof ^(p)D may be expanded into one that fragments Ω. More specifically,selected negative arcs corresponding to negative entries in the matrix^(p)D may be used to form cycles that generate a proper subgroup H of Ω.In turn, the group action H^(Ω) may split Ω into orbits that representthe diversification cells.

The GTTS processing may include a mechanism for ensuring that previouslyexplored elite solutions are not explored again. In particular, the GTTSprocessing may visit the orbits by utilizing a cross-cutting transversalT (also referred to herein as a diversification transversal). Theelements of the diversification transversal may index the orbits (thediversification cells) and when T is suitably small, may store dataindicating that the orbits have been visited. This may ensureanti-cycling and may avoid hash structures. Although transversal sizeand orbital sizes move in opposite directions, a transversal may beconstructed without having to construct an orbit. As a result, the groupaction may be chosen to produce a suitably short transversal. Forexample, a lesser number of negative entries may be chosen from ^(p)D toreduce the number of diversification cells that are constructed, therebyreducing the transversal size.

In certain example embodiments, assigning the exploration of eachdiversification cell to a different GPU thread may not be feasiblewithin a time constraint associated with an optimization problem sinceexploration of a diversification cell may be demanding. Rather, the GPUthreads may be used to explore a single diversification cell, with theGTTS module 114 managing movement along the diversification transversal.Exploration of a single diversification cell may include a short termmemory (STM) phase and an intensification phase of tabu search. The STMphase may include exploration of a diversification cell to determineelite solution(s). When an STM phase fails to produce any additionalelite solution, the GTTS processing may return to the most elitesolution determined thus far and may initiate an intensification phasein connection with the most elite solution. For example, the GTTSprocessing may initiate a new STM phase in connection with the mostelite solution. When that new STM phase fails to produce any additionalelite solution, the GTTS processing may again initiate the process atthe most elite solution. If that most elite solution is the same as apreviously chosen elite solution, the GTTS processing may insteadcontinue with the next best elite solution. Alternatively, the GTTSprocessing may initiate multiple new STM phases in parallel fromrespective multiple elite solutions.

The majority of the processing load on the GPU threads may occur duringthe STM phases of the GTTS processing. Since each GPU thread may explorethe same diversification cell Λ, the cell Λ may be split into smallersub-cells that are each probed in a parallel search by a correspondingGPU thread. A respective initial solution may be chosen for eachsub-cell to launch the GTTS processing with respect to each sub-cell.Although any equivalence relation on Λ may result in a fragmentation ofΛ, certain fragmentations may be more likely to yield elite solutionsand/or may be easier to process than others. In particular, anothergroup action may be used to construct a transversal that may be used tonavigate the smaller sub-cells while avoiding cycling. In turn, eachtransversal element may launch an STM phase of the GTTS processing thatis assigned to a corresponding GPU thread. Since each GPU threadexplores a different disjoint orbit, GPU threads may not be required tocommunicate with one another.

More specifically, since the group action _(H)Ω produced thediversification cells, any H-subgroup K yields the group action _(K)Λhaving orbits that fragment Λ. As long as H does not have a prime order,the GTTS module 114 may apply different H-subgroups to each of thediversification cells to achieve different fragmentations, each of whichmay be more appropriate to the cell's initial solution. In order toachieve this, H may need to have a suitably rich subgroup lattice fromwhich a choice of K can be made. This, however, may, in turn, affect hownegative arcs are chosen from ^(p)D to build the diversification cells.

FIG. 2 depicts an example hardware architecture of the supervisory CPU102 and an example hardware architecture of the GPU 104 in accordancewith one or more example embodiments of the disclosure. It should beappreciated that other hardware architectures of the CPU 102 and the GPU104 that may include additional and/or alternative hardware, firmware,and/or software components than the example hardware architecturesdepicted in FIG. 2 are also within the scope of this disclosure.

The supervisory CPU 102 may include a group of arithmetic logic units(ALUs) 202(1)-202(R). The supervisory CPU 102 may also include a cache206. The supervisory CPU 102 may be optimized to store and retrieve datafrom the cache 206 with a low latency. The supervisory CPU 102 mayfurther include a control unit 204 that is operatively coupled to thegroup of ALUs 202(1)-202(R) and the cache 206. The control unit 204 maybe configured to manage the utilization of the various ALUs202(1)-202(R) as well as manage the storage and retrieval of data in thecache 206.

The supervisory CPU 102 may be operatively coupled to one or more memorydevices such as, for example, a dynamic random access memory (DRAM) 208.The CPU 102 may be operatively coupled to the DRAM 208 via one or morebuses 218 such as, for example, one or more buses that utilize aPeripheral Component Interconnect (PCI) Express high-speed serialcomputer expansion bus standard. The one or more buses 218 may furtheroperatively couple the CPU 102 to the GPU 104, allowing data exchangebetween the CPU 102 and the GPU 104.

The GPU 104 may include a collection of ALUs 212(1)-212(T). In certainexample embodiments, the number of ALUs in the collection of ALUs212(1)-212(T) of the GPU 104 may be greater than the number of ALUs inthe collection of ALUs 202(1)-202(R) of the CPU 102, which may allow theGPU 104 to execute a greater number of parallel computations than theCPU 102. In particular, the GPU 104 may be more efficient at launchingmultiple processing threads and executing the threads in parallel thanthe CPU 102. The GPU 104 may further include a cache 216, one or morememory devices (e.g., video RAM (VRAM) 210), and a control unit 214 thatoperatively couples the collection of ALUs 212(1)-212(T), the VRAM 210,and the cache 216. The control unit 214 may be configured to manage theutilization of the various ALUs 202(1)-202(T) as well as manage thestorage and retrieval of data in the VRAM 210 and/or the cache 216. Thecache 206 of the CPU 102 may be larger than the cache 216 of the GPU 104to enable the CPU 102 to rapidly switch between execution jobs.

In certain example embodiments, the CPU 102 may serve as a host to theGPU 104, which may act as a coprocessor to the CPU 102. Data from theDRAM 208 may be copied to the VRAM 210 for use by the GPU 104 inperforming computations using the collection of ALUs 212(1)-212(T). Inparticular, the host (e.g., the CPU 102) may launch kernels on thecoprocessor (e.g., the GPU 104) and may also determine the number ofthreads needed to process an execution job in parallel on the GPU 104.After the GPU 104 executes the threads in parallel and completes theexecution job, the computational results may be stored in the VRAM 210and copied from the VRAM 210 to the DRAM 208. The CPU 102 may the accessthe computational result from the DRAM 208.

FIG. 3 depicts an example configuration of a streaming multiprocessor ofthe GPU 104 in accordance with one or more example embodiments of thedisclosure. In certain example embodiments, the streaming multiprocessordepicted in FIG. 3 may be a particular configuration of a GPU thread ofthe collection of GPU threads 128(1)-128(N) depicted in FIG. 1. Itshould be appreciated, however, that other configurations of a streamingmultiprocessor that may include additional and/or alternative hardware,firmware, and/or software components than the configuration depicted inFIG. 3 are also within the scope of this disclosure.

As depicted in FIG. 3, the streaming multiprocessor (SM) 302 may includean instruction unit 304 operatively coupled to a shared memory 306. TheSM 302 may include a group of streaming processors (SPs) 308(1)-308(S)operatively coupled to the instruction unit 304. Each SP 308(1)-308(S)may be referred to herein interchangeably as a core. The instructionunit 304 may distribute a set of instructions among the SPs308(1)-308(S), with each SP executing a single thread instruction. EachSP 308(1)-308(S) may include a multiply-add arithmetic unit configuredto perform single-precision floating-point operations. In addition, theSM 302 may include a group of special functional units (SFUs)310(1)-310(U) that may be configured to execute more complex arithmeticoperations with low cycle latency.

FIG. 4 depicts an example configuration of a thread processing cluster(TPC) of the GPU 104 in accordance with one or more example embodimentsof the disclosure. It should be appreciated that other configurations ofa TPC that may include additional and/or alternative hardware, firmware,and/or software components than the configuration depicted in FIG. 4 arealso within the scope of this disclosure. FIG. 5 depicts an exampleconfiguration of the GPU 104 in accordance with one or more exampleembodiments of the disclosure. It should be appreciated that otherconfigurations of the GPU 104 that may include additional and/oralternative hardware, firmware, and/or software components than theconfiguration depicted in FIG. 5 are also within the scope of thisdisclosure.

As shown in FIG. 4, a group of SMs 302(1)-302(U) may together compriseat least part of a thread processing cluster (TPC) 402. Any of the SMs302(1)-302(U) may have the example configuration of the SM 302 depictedin FIG. 3. Further, as depicted in FIG. 5, an example GPU architecturemay include a collection of TPCs 402(1)-402(V) operatively coupled to acollection of caches 504(1)-504(X) via an interconnection network 502.Any of the TPCs 402(1)-402(V) may have the example configuration of theTPC 402. The CPU 102 may allocate thread blocks to the GPU 104, whichmay, in turn, allocate each thread block to a respective TPC of thecollection of TPCs 402(1)-402(V). A respective one or more threads ineach thread block may be then be allocated among the various SMs302(1)-302(U) of the corresponding TPC (e.g., 402(1)) to which thethread block has been allocated.

It should be appreciated that the example hardware architectures andconfigurations depicted in FIGS. 3-5 are equally applicable to othertypes of processing units beside the GPU 104. For example, the examplehardware architectures and configurations depicted in FIGS. 3-5 areapplicable to any multiprocessor/accelerator designed to performaccelerated computation.

FIG. 6 is a process flow diagram of an illustrative method 600 forexecuting group theoretic tabu search (GTTS) processing to determine afinal solution to a program representative of an optimization problem inaccordance with one or more example embodiments of the disclosure. FIG.6 will be described in conjunction with FIG. 1 hereinafter.

At block 602, the pre-processor 108 may determine, based at least inpart on one or more constraints, a type of MP to utilize to represent anoptimization problem. For example, the pre-processor 108 may determinethe type of MP based at least in part on the input data/constraints 106.In particular, the pre-processor 108 may choose a particular type of MPto represent the optimization problem among candidate types of MPs. Thecandidate types of MPs may include a linear program, an integer program,a mixed integer program, a nonlinear program, a convex program, astochastic program, a dynamic program, or the like. For example, thepre-processor 108 may select an integer program to represent the n-city,m-TSP problem.

Upon selection of a type of MP to represent the optimization program tobe solved, at block 604, the pre-processor 108 may communicate anidentification of the selected type of MP to the master program module112. At block 604, the pre-processor 108 may further communicate a setof initial variables to the master program module 112. The masterprogram module 112 may be configured to determine a solution method touse to solve the selected type of program. For example, at block 606,the master program module 112 may determine that a tabu search method isto be utilized to solve the selected type of MP. More specifically, atblock 606, the master program module 112 may determine that a finalsolution to the program can be obtained using GTTS processing asdescribed herein in accordance with example embodiments of thedisclosure.

Example embodiments of the disclosure in which the optimization problemto be solved is the n-city, m-TSP optimization problem assume that themaster program module 112 selects a tabu search method to solve theoptimization problem. Accordingly, in such example embodiments, themaster program module 112 may initialize the GTTS program module 114 toperform GTTS processing to determine one or more elite solutions to theproblem represented by the selected type of MP from within a solutionspace and within a specified time constraint. A most elite solution(e.g., a solution that most minimizes or maximizes the one or moreobjective functions of the optimization problem) may be selected as afinal solution to the optimization problem and may be a globally optimalsolution but may not be confirmable as such.

At block 608, the GTTS module 114 may determine an initial solution tothe selected type of MP representative of the optimization problem to besolved. More specifically, at block 608, the GTTS module 114 maydetermine an initial solution as a current solution of the MP selectedas being representative of the optimization problem to be solved. Incertain example embodiments, the initial solution may be an elitesolution that satisfies halting criteria for halting the GTTSprocessing. For example, in the case of the n-city, m-TSP optimizationproblem, the initial solution may be a permutation representative of atour between the n cities, where the permutation contains one or moreDCFs, each DCF being representative of a subtour between a disjointsubset of the n cities, and where a length of the tour is deemed to besuitably optimized. Alternatively, the initial solution (e.g., aninitially chosen permutation) may be an optimal solution if no otherpermutation (e.g., tour) exists that has at least one arc that has anegative entry in ^(p)D.

In other example embodiments, the initial solution may not be an elitesolution that satisfies the halting criteria, in which case, the GTTSmodule 114 may determine an initial fragmentation of the solution spaceand may assign each solution space fragment to a respective GPU thread128(1)-128(N) for processing. In certain example embodiments, the GTTSmodule 114 may determine a respective initial solution for each solutionspace fragment. In certain example embodiments, the operations at blocks608-618 may correspond to processing performed by a particular GPUthread with respect to a particular solution space fragment. Morespecifically, the operations at blocks 608-618 may correspond to an STMphase of GTTS processing in accordance with example embodiments of thedisclosure.

At block 610, a GPU thread 128 may determine a neighborhood of solutionsassociated with a current solution. During a first iteration of the GTTSprocessing, the initial solution may be the current solution referencedat block 610. In certain example embodiments, the move methods that maybe used to determine the neighborhood at block 610 may be determinedfrom a recent history of previous move methods. For example, certainmoves may be temporarily restricted, a profile of desirable elitesolutions may be used to guide the move methods, and so forth. At block610, the move methods used to determine a neighborhood of solutionsassociated with the current solution may be chosen based on one or moreconstraints such as, for example, a constraint that cycle structure ofthe current solution is to be maintained, a constraint that a particularsubpath of the current solution is to be maintained, and so forth.

At block 612, the GPU thread 128 may select a member of the neighborhoodas a new current solution. In certain example embodiments, recent searchhistory may impact the new current solution selected at block 612.Further, a desire to preserve cycle structure, maintain relativepositions of specified disjoint p-subpaths, or the like may influencethe selection of the new current solution.

At block 614, the GPU thread 128 may update a set of elite solutions.For example, the GPU thread 128 may include the new current solution inthe set of elite solutions. Then, at block 616, the GPU 128 maydetermine whether halting criteria are satisfied for halting the GTTSprocessing being performed by the GPU 128. The halting criteria mayinclude, for example, whether a time constraint has been met, whether anelite solution has been obtained that satisfies an optimizationthreshold, whether a threshold number of iterations of the GTTSprocessing have been performed, or the like. In response to a negativedetermination at block 616, the method 600 may proceed iteratively fromblock 610. On the other hand, in response to a positive determination atblock 618, the GPU thread 128 may select a particular solution in theset of elite solutions as the final solution of the MP representative ofthe optimization problem based at least in part on one or more selectionparameters. For example, a GPU thread 128 may select an elite solutionthat minimizes or maximizes one or more objective functions of the MPamong the set of elite solutions.

FIG. 7 is a process flow diagram of an illustrative method 700 forfragmenting a solution space into a plurality of cells, fragmenting eachcell into a plurality of sub-cells, and providing each sub-cell to arespective GPU thread for executing GTTS processing in accordance withone or more example embodiments of the disclosure. FIG. 7 will bedescribed in connection with FIG. 1 hereinafter.

At block 702, the GTTS module 114 may fragment a solution space into aplurality of cells. Each cell may be a disjoint subset of the solutionspace. For example, the fragmentation performed at block 702 may splitthe solution space Ω (e.g., a symmetric group) into disjoint subsetsreferred to as cells. As previously described, an initial solution maydetermine the initial fragmentation of Ω. That is, negative entries inthe matrix ^(p)D (described in more detail hereinafter) may identify thearcs among which is one that yields a better solution than the initialsolution. This use of ^(p)D may be expanded into one that fragments Ω.More specifically, selected negative arcs corresponding to negativeentries in the matrix ^(p)D may be used to form cycles that generate aproper subgroup H of Ω. In turn, the group action _(H)Ω may split Ω intoorbits that represent the diversification cells.

The GTTS processing may include a mechanism for ensuring that previouslyexplored elite solutions are not explored again. In particular, atblock, the GTTS module 113 may determine a cross-cell transversal. TheGTTS processing performed by a GPU thread 128 may visit the orbits byutilizing the cross-cutting transversal T (also referred to herein as adiversification transversal). The elements of the diversificationtransversal may index the orbits (the diversification cells) and when Tis suitably small, may store data indicating that the orbits have beenvisited. This may ensure anti-cycling and may avoid hash structures.

In certain example embodiments, assigning the exploration of eachdiversification cell to a different GPU thread may not be feasiblewithin a time constraint associated with an optimization problem sinceexploration of a diversification cell may be demanding. Rather, the GPUthreads may be used to explore a single diversification cell, with theGTTS module 114 managing movement along the diversification transversal.Exploration of a single diversification cell may include a short termmemory (STM) phase and an intensification phase of tabu search. The STMphase may include exploration of a diversification cell to determineelite solution(s). When an STM phase fails to produce any additionalelite solution, the GTTS processing may return to the most elitesolution determined thus far and may initiate an intensification phasein connection with the most elite solution. For example, the GTTSprocessing may initiate a new STM phase in connection with the mostelite solution. When that new STM phase fails to produce any additionalelite solution, the GTTS processing may again initiate the process atthe most elite solution. If that most elite solution is the same as apreviously chosen elite solution, the GTTS processing may insteadcontinue with the next best elite solution. Alternatively, the GTTSprocessing may initiate multiple new STM phases in parallel fromrespective multiple elite solutions.

The majority of the processing load on the GPU threads may occur duringthe STM phases of the GTTS processing. Since each GPU thread may explorethe same diversification cell, the GTTS module 114 may select aparticular cell Λ of the plurality of cells at block 706, and mayfragment the cell Λ into a plurality of sub-cells at block 708. Eachsub-cell may then be explored by a corresponding GPU thread as part of aparallel search. In particular, at block 710, the GTTS module 114 maydetermine a respective initial solution for each of the plurality ofsub-cells. The GTTS module 114 may then provide each initial solution toa respective GPU thread 128 to perform GTTS processing on thecorresponding sub-cell.

At block 714, the GTTS module 114 may receive a respective elitesolution corresponding to each sub-cell. More specifically, the GTTSmodule 114 may receive the computational results from each GPU thread,where each GPU thread may have determined one or more elite solutionsbased at least in part on the GTTS processing performed on itscorresponding sub-cell. At block 716, the GTTS module 114 may determinewhether to diversify exploration of the solution space to another cell.In response to a positive determination at block 716, the method 700 mayproceed to block 706, where a new cell of the plurality of cells may beselected for fragmentation into a corresponding plurality of sub-cells.On the other hand, in response to a negative determination at block 716,the method 700 may proceed to block 718, where the GTTS module 114 mayselect each respective elite solution as a new initial solution for theGTTS processing performed by the various GPUs.

At block 720, the GTTS module 114 may determine whether halting criteriaare satisfied for halting the GTTS processing. In response to a negativedetermination at block 720, the method 700 may proceed iteratively fromblock 712. On the other hand, in response to a positive determination atblock 720, the method 700 may proceed to block 722, where the GTTSmodule 114 may select a particular elite solution as the final solutionto an MP representative of an optimization problem. The final solutionselected at block 722 may be selected based at least in part on one ormore selection parameters. For example, the final solution selected atblock 722 may be a most elite solution determined among all elitesolutions identified during the GTTS processing.

Referring again to the n-city, m-TSP problem for illustrative purposes,the final solution sought for this problem is a derangement (e.g., apermutation in which each element is mapped to an element other thanitself) having minimum tourlength. Accordingly, given an initialsolution represented by the permutation p and a candidate solutionrepresented by the permutation q, the GTTS processing may determinewhether q is an elite solution by determining whether q has a shortertourlength than p. Computing a tourlength involves many additions andwhen done numerous times during GTTS processing as described herein, thecomputational burden may be significant.

Accordingly, in certain example embodiments, the tourlength differencegiven by tourlength(q)−tourlength(p) may be computed since whennegative, the permutation q has a shorter tourlength. This tourlengthdifference may be computed without computing the individual tourlengthsof p and q since the lengths of common arcs cancel out in the tourlengthdifference leaving just the non-common arcs. The non-common arcs may bedetermined as those arcs whose tails are given by mov(qp⁻¹)=mov(pq⁻¹).This equality holds because (qp⁻¹)⁻¹=pq⁻¹ and a permutation and itsinverse move the same letters. In arc t→h, t and h are respectively thearc's tail and head. For an n× n, 0-diagonal distance matrix D, thetourlength of p∈S_(n) is the sum of its arclengths.

A mathematical formulation of this statement is shown below. In themathematical formulation below, k^(p) is the p-image of letter k.

$\mspace{20mu}{{{tourlength}\mspace{11mu}(p)} = {\sum\limits_{k = 1}^{n}{D\left( {k,k^{p}} \right)}}}$  Thus:$\Delta_{qp} = {{{{tourlength}\mspace{11mu}(q)} - {{tourlength}\mspace{11mu}(p)}} = {{{\sum\limits_{k}{D\left( {k,k^{q}} \right)}} - {D\left( {k,k^{p}} \right)}} = {{{\sum\limits_{k \in {{mov}{({qp}^{- 1})}}}{D\left( {k,k^{q}} \right)}} - {D\left( {k,k^{p}} \right)}} = {{\sum\limits_{k \in {{mov}{({qp}^{- 1})}}}}^{p}{D\left( {k,k^{q}} \right)}}}}}$Here, ^(p)D is a matrix whose (i, j)'th entry is D_(ij) minus D(i,i^(p)). In turn, Δ_(qp) is found by adding the entries of ^(p)D that qtraces over mov(q p⁻¹). Note that the main diagonal entries of ^(p)Dneed not be zero because if q isn't a derangement and doesn't movek∈mov(q p⁻¹) then^(p) D(k,k ^(q))=D(k,k ^(q))−D(k,k ^(p))=D(k,k)−D(k,k ^(p))=0−D(k,k^(p))=−D(k,k ^(p))

As an example, in S₅, let p=(1, 4) (2, 5, 3) and q=(2, 3, 4, 1). In thisexample, q is not a derangement since the element 5 maps to itself

Trace of ^(p)D traced by Distance Matrix D p = (1,4) (2,5,3) ^(p)D q =(2,3,4,1) $\quad\begin{pmatrix}0 & 15 & 1 & 68 & 4 \\66 & 0 & 98 & 69 & 75 \\16 & 25 & 0 & 91 & 84 \\71 & 2 & 31 & 0 & 26 \\45 & 74 & 70 & 57 & 0\end{pmatrix}$ $\quad\begin{pmatrix}0 & 15 & 1 & 68 & 4 \\66 & 0 & 98 & 69 & 75 \\16 & 25 & 0 & 91 & 84 \\71 & 2 & 31 & 0 & 26 \\45 & 74 & 70 & 57 & 0\end{pmatrix}$ $\quad\begin{pmatrix}{- 68} & {- 53} & 67 & 0 & {- 64} \\{- 9} & {- 75} & 23 & {- 6} & 0 \\{- 9} & 0 & {- 25} & 66 & 59 \\0 & {- 69} & {- 40} & {- 71} & {- 45} \\{- 25} & 4 & 0 & {- 13} & {- 70}\end{pmatrix}$ $\quad\begin{pmatrix}{- 68} & {- 53} & 67 & 0 & {- 64} \\{- 9} & {- 75} & 23 & {- 6} & 0 \\{- 9} & 0 & {- 25} & 66 & 59 \\0 & {- 69} & {- 40} & {- 71} & {- 45} \\{- 25} & 4 & 0 & {- 13} & {- 70}\end{pmatrix}$

With p=(1, 4) (2, 5, 3) and q=(2, 3, 4, 1), mov(qp⁻¹)=mov((1, 3) (2,5))={1, 2, 3, 5}. The trace of q over {1, 2, 3, 5} may then be computedto yield

$\quad\begin{pmatrix}x & 1 & 2 & 3 & 5 \\x^{q} & 2 & 3 & 4 & 5\end{pmatrix}$where each column gives the row/column location of the entry bolded inthe last matrix shown above. Adding the bolded entries in the lastmatrix, tourlength(q)−tourlength(p)=−53+23+66-70=−34. Alternatively,tourlength(q)=275, tourlength(p)=309 and 275-309=−34.

The utility of the formula for Δ_(qp) depends upon mov(qp⁻¹) and theprocessing capacity/time required to compute qp⁻¹. As mov(qp⁻¹) grows,the formula for Δ_(qp) may become less useful, ultimately potentiallyyielding no processing capacity/time savings over computing a fulltourlength. While this may generally be the case, example embodiments ofthe disclosure may transform p into q using methods that preserve muchof p. In turn, many common arcs cancel out in calculating the tourlengthdifference, thereby yielding a small mov(qp⁻¹).

Various mechanisms are available for transforming one permutation intoanother. Three such mechanisms are left permutation composition, rightpermutation composition, and conjugation. Assuming that m∈S_(n), leftpermutation composition of permutation p with permutation m may berepresented as q=mp. Thus qp⁻¹ (mp)p⁻¹=m and so mov(qp⁻¹)=mov(m). Insuch an example, there may be no need to compute qp⁻¹ since it movesonly those letters in m. As another example, right permutationcomposition of permutation p with permutation m may be represented asq=pm. Thus qp⁻¹ (pm)p⁻¹=m^(−p) and so qp⁻¹ has as many letters as msince conjugation preserves cycle structure. Note that if t→h is a p-arcthen t^(p)=h or equivalently, t=h^(−p). Thus the letters in m^(−p) arethe tails of the p-arcs whose heads are the letters in m. As anotherexample, conjugation of the permutation p with the permutation m may berepresented as q=p^(m). Thusqp⁻¹=p^(m)p⁻¹=(m⁻¹pm)p⁻¹=m⁻¹(pmp⁻¹)=m⁻¹m^(−p), thereby indicating thatqp⁻¹ moves at most twice the letters in m.

A fourth mechanism for transforming a permutation into anotherpermutation is to raise a permutation to a power. One mechanism forbuilding a neighborhood of p is to build <p>, the smallest subgroup thatcontains p. For instance, the tables below (in which ( ) is theidentity) show <p> for different permutations p:

TABLE 1 m p^(m) 1 (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) 2 (1, 3, 5, 7,9, 11)(2, 4, 6, 8, 10, 12) 3 (1, 4, 7, 10)(2, 5, 8, 11)(3, 6, 9, 12) 4(1, 5, 9)(2, 6, 10)(3, 7, 11)(4, 8, 12) 5 (1, 6, 11, 4, 9, 2, 7, 12, 5,10, 3, 8) 6 (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12) 7 (1, 8, 3, 10, 5,12, 7, 2, 9, 4, 11, 6) 8 (1, 9, 5,)(2, 10, 6)(3, 11, 7)(4, 12, 8) 9 (1,10, 7, 4)(2, 11, 8, 5)(3, 12, 9, 6) 10 (1, 11, 9, 7, 5, 3)(2, 12, 10, 8,6, 4) 11 (1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2) 12 ( )

TABLE 2 m p^(m) 1 (1, 2, 3)(4, 5, 6, 7) 2 (4, 6)(5, 7)(1, 3, 2) 3 (4, 7,6, 5) 4 (1, 2, 3) 5 (1, 3, 2)(4, 5, 6, 7) 6 (4, 6)(5, 7) 7 (1, 2, 3)(4,7, 6, 5) 8 (1, 3, 2) 9 (4, 5, 6, 7) 10 (4, 6)(5, 7)(1, 2, 3) 11 (1, 3,2)(4, 7, 6, 5) 12 ( )

TABLE 3 m p^(m) 1 (1, 2, 3, 4, 5, 6, 7) 2 (1, 3, 5, 7, 2, 4, 6) 3 (1, 4,7, 3, 6, 2, 5) 4 (1, 5, 2, 6, 3, 7, 4) 5 (1, 6, 4, 2, 7, 5, 3) 6 (1, 7,6, 5, 4, 3, 2) 7 ( )

In the bolded rows of Table 1, p^(m) has p's cycle structure because mis coprime to 12=order(p). The last table is a special instance of thissince the prime number 7 is coprime to the smaller numbers. So, if cyclestructure must be preserved then these coprime powers will do so.Otherwise, the DCFs of p^(m) have the same length that divides order(p).The resulting cycle structures can be transformed using templates(permutations that split and merge other permutations) to yieldpermutations that have a target cycle structure. Given n-cyclesp,q∈S_(n), the solution space of p^(x)=q depends upon the subgroupgenerated by p (e.g., <p>).

In certain example embodiments, if cycle structure is to be preserved,then conjugation may be the move method of choice for GTTS processing.More specifically, to move from a permutation p to a permutation qhaving the same cycle structure as p, a permutation x that satisfiesp^(x)=q may be sought. Several such permutations x may exist since thesolution space is the right coset cent_(p)r for cent_(p) (thecentralizer of p in S_(n)) and r (any specific solution). An exampleapproach for determining an r may be to align (in a 2-row matrix) thegiven p and q on their DCFs, strike the cycle boundaries, and then viewthe resulting table as a standard form permutation. For instance, ifp=(4, 2) (1, 5, 3) and q=(2, 4, 1) (3, 5):

$\begin{pmatrix}{\left( {4,2} \right)\mspace{11mu}\left( {1,5,3} \right)} \\{\left( {2,4,1} \right)\mspace{11mu}\left( {3,5} \right)}\end{pmatrix}\overset{align}{=}{\begin{pmatrix}{\left( {4,2} \right)\mspace{11mu}\left( {1,5,3} \right)} \\{\left( {3,5} \right)\mspace{11mu}\left( {2,4,1} \right)}\end{pmatrix}\underset{boundaries}{\overset{strike}{=}}{\begin{pmatrix}4 & 2 & 1 & 5 & 3 \\3 & 5 & 2 & 4 & 1\end{pmatrix} = {\left( {4,3,1,2,5} \right) = r}}}$Thus q=p^(r), i.e., ((4, 2) (1, 5, 3))^((4,3,1,2,5))=(2, 4, 1)(3, 5).In the case of an n-city 1-TSP, cent_(p)=<p>. For instance, in S₆ withp=(3, 1, 2, 6, 5, 4) and q=(6, 1, 3, 5, 2, 4), the solution space ofp^(x)=q is cent_(p) r:

$r = {\begin{pmatrix}3 & 1 & 2 & 6 & 5 & 4 \\6 & 1 & 3 & 5 & 2 & 4\end{pmatrix} = \left( {3,6,5,2} \right)}$${cent}_{p} = {{< p>=\left\{ {p,p^{2},p^{3},p^{4},p^{5},{p^{6} = e}} \right)} = {\begin{matrix}\left( {1,2,6,5,4,3} \right) \\{\left( {1,4,6} \right)\mspace{11mu}\left( {2,3,5} \right)}\end{matrix}{\begin{matrix}{\left( {1,6,4} \right)\mspace{11mu}\left( {2,5,3} \right)} \\\left( {1,3,4,5,6,2} \right)\end{matrix}}\begin{matrix}{\left( {1,5} \right)\mspace{11mu}\left( {2,4} \right)\mspace{11mu}\left( {3,6} \right)} \\(\mspace{14mu})\end{matrix}}}$The solution space is the right coset

${{cent}_{p}r} = {\left\{ {{cr}:{c \in {cent}_{p}}} \right\} = {\begin{matrix}{\left( {1,3} \right)\mspace{11mu}\left( {2,5,4,6} \right)} \\\left( {1,4,5,3,2,6} \right)\end{matrix}{\begin{matrix}\left( {1,5,6,4} \right) \\\left( {1,6,3,4,2} \right)\end{matrix}}\begin{matrix}\left( {1,2,4,3,5} \right) \\\left( {2,3,6,5} \right)\end{matrix}}}$Thus for any x in the above coset, (3, 1, 2, 6, 5, 4)^(x)=(6, 1, 3, 5,2, 4)

Accordingly, choosing different permutations x from the above coset canresult in diversification of the GTTS processing. Another implication isthat a new search can begin on moves rather than TSP tours. That is,rather than having a GPU thread probe conjugates of p, a GPU thread mayinstead probe any transversal of the right cosets of cent_(p). When thissearch yields s as the optimal transversal element, p^(s) may be theoptimal tour in p's conjugacy class. The most optimal approach forsearching the transversal may not be known, but the indexing set ofΔ_(qp) and the form of ^(p)D may suggest an approach.

In accordance with example embodiments of the disclosure, a transversalmay be constructed of the right cosets of the centralizer of p=(1, 2, 3,4, 5) in S₅. Because p is a 5-cycle in S₅, its centralizer in S₅ is <p>whose order is 5. Per Lagrange's Theorem, there are 5!/5=4!=24 cosets.Any transversal T of the cosets may be constructed, and the GTTSprocessing may be shifted away from the tours to the transversal T. Theelements of the transversal T have diverse cycle structures that can bechosen to move a minimal number of letters. p^(T)k may be the tourassociated with the k'th transversal element. More specifically, anyelement chosen from that coset yields the same tour, consumes lessmemory than the tour, and no more memory than another coset member.

Example Carrier Dispatch Optimization

In one implementation, the methods, systems and operations describedherein may be utilized for carrier dispatch optimizations. A multiplecarrier dispatch optimization architecture may be utilized to ensurethat one or more vehicles (e.g., cars, trucks, vans, automobiles,motorcycles, off-road vehicles, boats, recreational vehicles (RVs),machinery, and/or the like) are optimally transported (e.g., shipped,moved, picked up, delivered, and/or the like) by one or more carriers(e.g., shippers, truckers, deliverers, and/or the like) following one ormore vehicle transactions (e.g., sales, purchases, trades, manufactures,gifts, repossessions, leases, and/or the like). In some embodiments, acarrier may include a fleet of carriers, or may include an individualand/or independent carrier. In one example, each carrier truck may becapable of transporting or carrying a different number of vehicles(1, 3,5, 10 and/or the like).

For example, if a first vehicle is purchased from a seller in Atlantaand needs to be transported to a first purchaser in New York, and asecond vehicle is purchased from the seller in Atlanta and needs to betransported to a second purchaser in Boston, the multiple carrierdispatch optimization architecture may be utilized to determine anoptimal delivery route for each vehicle using one or more carriers.Continuing with the example, the first and second vehicles may beassigned by the multiple carrier dispatch optimization architecture to afirst carrier to transport both of the first and second vehicles fromAtlanta to the Northeast. The first carrier may pick up the first andsecond vehicles in Atlanta, drive to New York and deliver the firstvehicle to the first purchaser, and then continue driving to Boston todeliver the second vehicle to the second purchaser. Alternatively, thefirst and second vehicles may be assigned by the multiple carrierdispatch optimization architecture to the first carrier to transportboth of the first and second vehicles from Atlanta to New York only. InNew York, the first carrier may deliver the first vehicle to the firstpurchaser in New York, and then may drop off the second vehicle in NewYork, where the second vehicle is to be picked up by a second carrier.The second vehicle may be assigned by the multiple carrier dispatchoptimization architecture to a second carrier to transport the secondvehicle from New York to Boston to therefore deliver the second vehicleto the second purchaser in Boston. In this manner, one or more vehiclesmay be assigned to one or more carriers by the multiple carrier dispatchoptimization architecture to ensure optimal transportation of the one ormore vehicles from respective first locations to respective secondlocations.

Additionally, if a carrier is currently scheduled to drive from Atlantato Boston and is planning to stop in New York to deliver a vehicle onthe way from Atlanta to Boston, the carrier may utilize the multiplecarrier dispatch optimization architecture to identify another vehiclein New York that needs to be delivered to Boston. In this manner, thecarrier is enabled to more efficiently schedule pick-ups and/ordeliveries along a route.

FIG. 8 illustrates an example system environment 800 for a multiplecarrier dispatch optimization, according to an embodiment of thedisclosure. The system environment 800 typically includes at least oneuser application 810, which may be accessed and/or controlled by a user.In some embodiments, the system environment 800 includes multiple userapplications 810 as depicted in FIG. 8 for enabling multiple users toutilize the multiple carrier dispatch optimization architecture.

In some embodiments, the user typically includes a carrier (e.g., ashipper, a cargo trucker, a driver, a carrier dispatcher, and/or thelike), but may also include a seller, a purchaser, a gifter, a giftee, atrader, an auctioneer, a repossessor, and/or the like of a vehicle,and/or the like. The user may utilize the user application 810 toinitiate operation of the multiple carrier dispatch optimizationarchitecture by providing one or more carrier objectives and/or carrierconstraints. For example, the user may input and/or upload one or morecarrier objectives and/or carrier constraints to the user application810. Alternatively, carrier objectives and/or carrier constraints may bereceived from a third party, or by scraping (e.g., automaticallyretrieving information from) one or more social media accounts, emailaccounts, user preferences of one or more online accounts, carrierdatabases, and/or the like.

Carrier objectives and/or carrier constraints may include routeinformation such as a start location, a destination location, a currentlocation, a start date and/or time, an ending date and/or time, anactive region (e.g., a territory of states) of operation, locations toavoid, and/or the like. Further, carrier objectives and/or carrierconstraints may be directed to carrier type such as a truck selection, atruck make and/or model, a trailer make and/or model, a truck size, atrailer size, a maximum quantity of vehicles and/or a maximum weightthat the carrier is enabled to transport (e.g., a carrier capacity),maximum dimensions for a carrier payload, possible vehicle loadingconfigurations of the carrier, a year of the carrier, gas mileage of thecarrier, an insurance status of the carrier, and/or the like. Carrierobjectives and/or carrier constraints may also include particularconstraints for unique abilities of a carrier, such as the carrier beingenclosed, being able to carry an inoperable vehicle, being able to carrya particular type of vehicle (e.g., a motorcycle, a boat, and/or car),and/or the like. Further, if a carrier has multiple slots for multiplevehicles, the user may denote carrier constraints for each individualslot. For example, a first slot of a carrier may be configured fortransporting a motorcycle, while a second slot of a carrier may beconfigured for transporting a boat. Further, one slot may be configuredto transport different vehicle types. In some embodiments, specifichardware (e.g., straps, modification equipment, and/or the like), may benecessary for modifying a slot for transporting a first vehicle of afirst vehicle type so that, after modification, the slot may transport asecond vehicle of a second vehicle type. Accordingly, this modifyingability of slots may be included as carrier objectives and/or carrierconstraints. Additionally, carrier objectives and/or carrier constraintsmay also include constraints related to the Department of Transportation(DOT), such as the carrier not being allowed to travel on particularroads due to weight, truck size, and/or the like. Further carrierobjectives and/or carrier constraints may include various import and/orexport regulations associated with crossing from one location intoanother (e.g., from country to country, and/or the like). In someembodiments, particular carrier objectives and/or constraints may berequired by the user application 810, or in other embodiments may beoptional.

The at least one user application 810 typically communicates with aninventory manager 120. For example, the at least one user application810 may provide carrier objectives and/or carrier constraints receivedfrom the user to the inventory manager 820 for processing.

The inventory manager 820 typically includes vehicle records of allavailable vehicles to be transported. A vehicle record typicallyincludes information and/or attributes associated with a vehicle such asan internal identification number (ID), a vehicle identification number(VIN), a year, a make, a model, trim, a weight, a size, an operablestatus, an enclosed status, a pickup address (e.g., street, city, state,ZIP, and/or the like), a pickup region, a delivery address (e.g.,street, city, state, ZIP, and/or the like), a delivery region, a startdate and/or time, and/or the like. Information and/or attributesassociated with a vehicle may further include information associatedwith a party (e.g., a shipper, a purchaser, a seller, and/or the like)in a vehicle transaction involving the vehicle such as a purchase order(PO) number, account information, an address, a shipping and/or deliveryprice, a segment price (e.g., a price of transporting a vehicle along asegment of a particular route, such as a segment between Baltimore andPhiladelphia on a route from Atlanta to New York, or a portion of atransport that may be accomplished by another mode, for instance aportion in which the vehicle is moved by train or boat), and/or thelike. Information and/or attributes of a vehicle may also include anamount of time that the vehicle has been in queue, progress, and/orstaging in the multiple carrier dispatch optimization architecture.Information and/or attributes associated with one or more vehicles maybe provided by a party involved in a vehicle transaction, by scraping avehicle database associated with a vendor, a VIN decoding database,wholesale auction databases, vehicle inspection databases, manufacturer,a seller, a dealership, a broker, and/or the like, and/or in a varietyof other ways. In some embodiments, information and/or attributesassociated with one or more vehicles may be imported from one or moredatabases.

The inventory manager 820 typically processes received carrierobjectives and/or carrier constraints to identify one or more vehiclerecords of one or more vehicles that are available to the carrier basedon the carrier objectives and/or carrier constraints provided by theuser (e.g., received from the user application 810). For example, theinventory manager 820 may filter and/or sort one or more vehicle recordsof one or more vehicles based on a comparison of received carrierobjectives and/or carrier constraints and information and/or attributesincluded in the one or more vehicle records of one or more vehicles. Insome embodiments, the inventory manager 820 may determine at least apartial match between carrier objectives and/or carrier constraints andinformation and/or attributes included in the one or more vehiclerecords of one or more vehicles. Determining at least a partial matchbetween carrier objectives and/or carrier constraints and informationand/or attributes may cause the inventory manager 820 to determine thatone or more vehicle records of one or more vehicles are eligible (e.g.,available) to be transported by the carrier. In some embodiments, theinventory manager 820 may generate a listing of all vehicle records(e.g., vehicles) that are available for transport by the carrier. Thelisting may be sorted and/or ranked based on a calculated score of eachavailable vehicle record, where the calculated score corresponds to abenefit, cost, price, and/or the like of transporting each availablevehicle record. In some embodiments, the calculated score may bedetermined by the inventory manager 820 based on determining at least apartial match between carrier objectives and/or carrier constraints andinformation and/or attributes of each vehicle, a price, a cost, aprofit, and/or the like of the carrier transporting each vehicle, and/orthe like. Also, the calculated score of a vehicle and/or segment may becompared to one or more threshold values corresponding to a likelihoodof acceptance by the carrier and/or inclusion in one or more optimizedsolution sets.

The inventory manager 820 may, after identifying one or more vehiclerecords of one or more vehicles that are available to the carrier basedon carrier objectives and/or carrier constraints, transmit the one ormore vehicle records of the one or more vehicles determined to beavailable to the carrier to an optimizer 830 for processing. Theinventory manager 820 may also transmit the carrier objectives and/orcarrier constraints, information and/or attributes comprised in the oneor more vehicle records of the one or more vehicles to the optimizer 830for processing. In some embodiments, the one or more vehicle records ofthe one or more vehicles determined to be available to the carrier maybe transmitted from the inventory manager 820 to the optimizer 830 via adata stream of one or more data packets, by generating a downloadablefile, uploading the file to a service, and transmitting a link whichallows a download of the file to be initiated, and/or the like.

The optimizer 830 may process information received from the inventorymanager 820 to generate one or more optimized solution sets of vehicleloads for the carrier based on the information received from theinventory manager 820 (e.g., vehicle records, carrier objectives and/orcarrier constraints, information and/or attributes included in the oneor more vehicle records of the one or more vehicles, and/or the like).For example, the optimizer 830 may group together (e.g., bundle) one ormore vehicles based on a common pick-up and/or delivery location, thecalculated score of each available vehicle, and/or the like. Theoptimizer 830 may further identify one or more matches of informationand/or attributes included in the one or more vehicle records of the oneor more vehicles. Alternatively, the optimizer 830 may bundle one ormore vehicles based on an estimated delivery price and/or route segmentprice in a way that maximizes an amount of carrier profit, minimizes adistance to be traveled when a carrier is loaded below capacity, a cost,minimizes a distance between a scheduled pick-up and/or deliverylocation of one or more vehicles included in an optimized solution setand an existing carrier location and/or planned route, maximizes adispatch and/or carrier revenue per day and/or revenue per mile, and/oran amount of time for the carrier to transport vehicles included in theone or more optimized solution sets, and/or provides other benefits tothe carrier. In this manner, vehicles may be grouped and/or bundledtogether into an optimized solution set that provides one or moreoptimal routes of transporting the included vehicles. The one or moreoptimized solution sets of vehicle loads for the carrier may include oneor more routes for the carrier to pick up and/or deliver (e.g.,transport) one or more vehicles identified by the inventory manager 820as available to be transported by the carrier. For example, the one ormore optimized solution sets may include a list of vehicles availablefor pick-up and/or delivery at particular locations and/or along aparticular carrier route.

For example, the optimizer 830 may determine a total dispatch profit ofan optimized solution set by summing revenue associated withtransporting each vehicle included in the optimized solution set andthen subtracting carrier cost associated with transporting each vehicleincluded in the optimized solution set, wherein cost associated withtransporting each vehicle may be determined by multiplying a totaldistance traveled by a carrier cost per mile. Additional factors thatare utilized to determine a dispatch profit of one or more vehiclesand/or vehicle segments may include a length of a route, a pick-uplocation, a delivery location, a shipping cost, a carrier cost, uniqueloading constraints, licensing/permitting requirements, and/or the like.Weights may be assigned to one or more variables and/or factors when adetermining profit and/or cost of transporting a vehicle (e.g., avehicle segment). The optimizer 830 may then compare each determinedtotal dispatch profit of all solution sets generated for the user (e.g.,carrier) to determine an optimized solution set that has a highestdispatch profit.

It is noted that the optimizer 830 may not only aim to maximize profitfor each carrier, but may also aim to maximize profit for a dispatcherassociated with the system environment 800 described herein. Forexample, each vehicle may be associated with a cost for transportallocated by a selling party (or donating party, trading party,purchasing party, and/or the like) and/or a selling platform (e.g., anauction house and/or website, an online marketplace, and/or the like)and a cost associated with a carrier actually transporting each vehicle.The optimizer 830 typically seeks to minimize the cost associated withthe carrier while maximizing the cost for transport allocated by theselling party. In some embodiments, these costs may be fixed and/ordynamic based on a variety of conditions such as supply and demand,market value of a vehicle, time of year, month, week, day, and/or thelike, weather conditions, carrier constraints and/or carrier objectives,vehicle attributes and/or information, and/or the like. In this manner,the optimizer 830 may be focused on providing a dispatcher-centricsystem for maximizing dispatch profits by optimally allocating one ormore vehicles to be transported by one or more carriers to a minimumnumber of carriers. Therefore, the system environment 800 andembodiments disclosed here differ from a typical carrier-centric system,such as a delivery service optimization system. As opposed to assigninga set of known packages for optimized delivery by one or more trucks asmay be done by a carrier-centric system, the system environment 800 ofthis disclosure may focus on selecting particular packages (e.g.,vehicles) to be optimally assigned to one or more trucks (e.g.,carriers) so as to maximize profits.

Upon generation, the one or more optimized solution sets may betransmitted from the optimizer 830 to the inventory manager 820, whichmay transmit the one or more optimized solution sets to the one or moreuser applications 810 for presentation to the user. The user (e.g., thecarrier) may then review the one or more optimized solution sets and/orselect one or more solution sets from the one or more optimized solutionsets using the one or more user applications 810. In some embodiments,transmitting the one or more optimized solution sets may includegenerating an alert (e.g., a vibration, a visual alert, an auditoryalert, and/or the like) and transmitting the alert in a message (e.g.,an email, a text message, and/or the like) to the inventory manager 820and/or the user via the one or more user applications 810.

The user may also be enabled to provide adjustments and/or modificationsto the one or more optimized solution sets. For example, the user mayadd, delete, remove, swap, trade, and/or the like one or more vehiclesincluded in the one or more optimized solution sets. In someembodiments, the user may initiate a request to trade one or morevehicles included a first optimized solution set with one or morevehicles included in a second optimized solution set. The user may alsobe presented with trade offers and/or suggested vehicles to be added,deleted, swapped, and/or the like by the one or more user applications810. For example, one or more vehicles may be recommended to the userfor selection and/or for addition to an optimized solution set.Suggestions of vehicles may be based on a variety of variables,information, and/or heuristics as disclosed herein, such as carrierconstraints and/or carrier objectives, vehicle information and/orvehicle attributes, profit, cost, distance, location, density ofvehicles in a particular location, and/or the like. In some embodiments,the user may be enabled to accept a trade offer for one or more vehiclesfrom another user and/or carrier, and multiple users may be enabled tocommunicate with one another via the one or more user applications 810,such as a via an instant messaging system. In this manner, the one ormore optimized solution sets may be further customized and/or optimizedto preferences and/or desires of the user (e.g., carrier), thereforeincreasing efficiency and maximizing profit of the carrier whentransporting the one or more vehicles included in a selected optimizedsolution set.

Typically, when a vehicle is included in an optimized solution set, thevehicle is exclusively included in the optimized solution set. Forexample, a vehicle record of a vehicle may be included in only oneoptimized solution set, which can then be accepted or rejected by theuser. Including a vehicle in an optimized solution set typicallyincludes removing a vehicle record of the vehicle included in theoptimized solution set from the inventory manager 820 so that thevehicle record of the vehicle is no longer available for inclusion in asecond optimized solution set. Alternatively, a vehicle record of avehicle may be included in one or more optimized solution sets.

In response to a user selection of one or more optimized solution sets,the inventory manager 820 may assign information associated with thecarrier (e.g., carrier objectives and/or carrier constraints) toinformation associated with the selected one or more optimized solutionsets (e.g., information and/or attributes included in the one or morevehicle records of the one or more selected vehicles). In this manner,vehicles included in the selected one or more optimized solution setsmay be assigned by the inventory manager 820 to the carrier fortransport. Alternatively, vehicle profiles of vehicles included in oneor more optimized solution sets that were not selected by the user maybe transmitted and/or returned to the inventory manager 820 forprocessing and/or inclusion in another optimized solution set by theoptimizer 830.

During the above-mentioned processes, information (e.g., carrierobjectives and/or carrier constraints, information and/or attributesincluded in one or more vehicle records of one or more vehicles, and/orthe like) may be transmitted to and/or received from the one or moreuser applications 810, the inventory manager 820, the optimizer 830,and/or an archival database 840. The archival database 840 may becontinuously updated and/or updated at predetermined intervals withinformation from various elements of the system environment 800. In thismanner, information stored in the archival database 840 may be utilizedin various post-processing analyses. For example, the archival database840 may receive and/or store the one or more selected optimized solutionsets for later recall by the user.

FIG. 9 is an example process flow diagram 900 illustrating details of anexample method for optimally assigning a vehicle to a carrier fordispatch, according to one embodiment of the disclosure. The diagram 900begins with receiving an order of a vehicle from a shipper (e.g., aseller, a buyer, a dealer, a broker, and/or the like) associated with avehicle transaction. In some embodiments, the order is received at theone or more user applications 810 and/or from a system associated withfacilitating vehicle transactions such as an auction website, adealership website, an online marketplace, and/or the like. In someembodiments, receiving the order includes receiving informationassociated with the vehicle and/or the vehicle transaction such asinformation and/or attributes to be included in a vehicle record of thevehicle. Receiving the order typically includes generating a vehiclerecord of the vehicle using information and/or attributes of thevehicle. The vehicle record may be generated by the one or more userapplications 810 and/or transmitted to the inventory manager 820 forgeneration by the inventory manager 820.

Again, a vehicle record typically includes information and/or attributesassociated with the vehicle. For example, a vehicle record of a vehiclemay include an internal identification number (ID), a vehicleidentification number (VIN), a year, a make, a model, a weight, a size,aftermarket features that alter stock weight and/or dimensions, anoperable status, an enclosed status, a pickup address (e.g., street,city, state, ZIP, and/or the like), a pickup region, a delivery address(e.g., street, city, state, ZIP, and/or the like), a delivery region, astart date and/or time, and/or the like. Information and/or attributesassociated with a vehicle and included in a vehicle record may furtherinclude information associated with a party (e.g., a shipper, apurchaser, a seller, a buyer, and/or the like) in a vehicle transactioninvolving the vehicle such as a purchase order (PO) number, accountinformation, an address, a shipping and/or delivery price, a segmentprice (e.g., a price of transporting a vehicle along a segment of aparticular route, such as a segment between Baltimore and Philadelphiaon a route from Atlanta to New York), a calculated score, and/or thelike. Information and/or attributes of a vehicle included in a vehiclerecord may also include an amount of time that the vehicle has been inqueue, progress, and/or staging in the multiple carrier dispatchoptimization architecture.

Once generated, the vehicle record of the vehicle may be placed into astaging queue for verification at block 810. The vehicle record of thevehicle is typically selected and/or verified by the one or more userapplications 810 and/or the inventory manager 820. In some embodiments,verifying the vehicle record of the vehicle includes determininginformation and/or attributes included in the vehicle record of thevehicle are valid based on a comparison of information and/or attributesincluded in the vehicle record of the vehicle and information and/orattributes stored in the archive database 840 (and/or other informationdisclosed herein). If information and/or attributes included in thevehicle record of the vehicle are determined to be invalid, the vehiclerecord (e.g., the vehicle) may be disqualified for inclusion in avehicle inventory of the inventory manager 820 and therefore may bediscarded at block 920. The vehicle record of the vehicle may also bedisqualified at any time. Conversely, if information and/or attributesincluded in the vehicle record of the vehicle are determined to bevalid, then the vehicle record of the vehicle is verified for inclusionin the vehicle inventory of the inventory manager 820.

Upon its verification, the vehicle record of the vehicle is transmittedto the inventory manager 820 for inclusion of the vehicle record of thevehicle in the vehicle inventory of the inventory manager 820 at block930. From the vehicle inventory of the inventory manager 820, thevehicle record of the vehicle (e.g., the vehicle) may be assigned to aparticular carrier in a variety of ways. Typically, assigning thevehicle to a carrier includes determining, based at least in part on ananalysis and/or a comparison of information and/or attributes includedin the vehicle record of the vehicle and/or carrier objectives and/orcarrier constraints, that the vehicle can be transported by the carrier(e.g., that the carrier is enabled to safely transport the vehiclewithin defined constraints).

For example, the inventory manager 820 may directly assign the vehicle(e.g., the vehicle record of the vehicle) from the vehicle inventory ofthe inventory manager 820 to a carrier for transportation of the vehicleby the carrier. Typically, a vehicle is directly assigned to a carrierin response to the carrier selecting an optimized solution set (or oneor more segments of a route, and/or the like) that includes the vehicle.As such, the vehicle is dispatched to the carrier for transportation ofthe vehicle by the carrier at block 940. In some embodiments,dispatching the vehicle to the carrier includes transmitting informationand/or attributes included in the vehicle record of the vehicle to thecarrier and/or the user by the one or more user applications 810, and/orthe like.

As a second example, the vehicle may be assigned as a single segment(e.g., a single route from a pick-up location of the vehicle to adelivery location of the vehicle) by the inventory manager 820 to anonline marketplace with which the system environment 800 is incommunication. For example, at block 950, the online marketplace mayinclude a listing and/or queue of available vehicles and/or vehiclesegments from which multiple carriers may select for transportation. Insome embodiments, the user may select a single vehicle (e.g., a singlesegment), multiple vehicles (e.g., multiple segments), an optimizedsolution set of vehicles (e.g., segments), and/or the like from theonline marketplace listing. In this manner, multiple carriers may selectmultiple vehicles for transportation from the online marketplaceaccording to carrier preferences such as a segment distance, segmentlocation and/or region, price, and/or the like. If the vehicle isselected by a carrier from the listing, the vehicle is assigned by theinventory manager 820 to the carrier that selected the vehicle, and thevehicle is dispatched at block 940. If the vehicle is not selected for apredetermined period of time during which the vehicle is available, thevehicle may be removed from the listing of the online marketplace and bereintroduced and/or re-included into the vehicle inventory of theinventory manager 820.

As a third example, the inventory manager 820 may communicate with theoptimizer 830 and/or transmit the vehicle record of the vehicle and/orinformation and/or attributes included in the vehicle record of thevehicle to the optimizer 830 for processing. In this manner and at block960, the optimizer 830 is enabled to include, potentially, the vehiclerecord (e.g., the vehicle and/or information and/or attributes of thevehicle) in one or more optimized solution sets of carrier loads and/orcarrier routes when determining the one or more optimized solution setsof carrier loads and/or carrier routes. The one or more optimizedsolution sets may be presented to the user and/or a carrier, who mayaccept or reject the one or more optimized solution sets, by the one ormore user applications 810. If an optimized solution set that includesthe vehicle is rejected, then the vehicle may be reintroduced and/orre-included into the vehicle inventory of the inventory manager 820 atblock 930. In some embodiments, the user (e.g., a carrier) may selectonly a portion of an optimized solution set. For example, the user mayselect a first and a second segment of a suggested optimal route, whilerejecting a third segment of the route. The third segment and associatedvehicles may be reintroduced and/or re-included into the vehicleinventory of the inventory manager 820 (or traded with another carrier)at block 930. Conversely, if an optimized solution set that includes thevehicle is accepted, then, at block 840, the vehicle is dispatched tothe user and/or carrier that selected the optimized solution set thatincludes the vehicle.

Typically, when the optimizer 830 includes the vehicle in one or moreoptimized solution sets at block 960, the vehicle's inclusion in the oneor more optimized solution sets is exclusive. For example, once avehicle included in a possible optimized solution set, the vehicle maynot be included in another optimized solution set until the optimizedsolution set that includes the vehicle is rejected by the user and/orthe carrier, in which case the vehicle and/or the vehicle record isreintroduced and/or re-included into the vehicle inventory of theinventory manager 820. Further, once a vehicle is selected by the userand/or a carrier from the listing of the online marketplace at block 950and/or dispatched to a carrier at block 940, the vehicle cannot beselected by another user and/or another carrier. In this manner, thevehicle may not be mistakenly assigned to multiple users and/orcarriers.

However, in some embodiments, one vehicle may be assigned to a pluralityof optimized solution sets. To prevent duplicity in assigning the onevehicle to multiple carriers for transport, the one vehicle may beassigned to the carrier associated with a user who first selects anoptimized solution set that includes the one vehicle. Accordingly, theoptimizer 830 may monitor, track, compare, and/or store one or moretime-stamps associated with each user's selection of each optimizedsolution set.

FIG. 10 is an example process flow diagram illustrating details of anexample method 300 for enabling a carrier to select an optimal vehicleshipment route, according to one embodiment of the disclosure. Thediagram begins at block 1005 with the user (e.g., a carrier) accessingthe one or more user applications 810. In some embodiments, the user mayaccess the one or more user applications 810 using a smart phone, atablet, a wearable device, a desktop computer, a laptop computer, aportable computing device, and/or the like.

Upon accessing the one or more user applications 810 for a first time,the user may be required and/or prompted by the one or more userapplications 810 to create an account at block 310. Creating an accountmay, in some embodiments, include defining one or more carrierobjectives and/or carrier constraints at block 1015 and/or as disclosedherein.

For subsequent accessing of the one or more user applications 810, theuser, at block 320, logs into the created account. Once logged in, theuser may be presented with a dashboard and/or landing page from whichthe user may select various actions and/or operations to be executed.For example, the user may enabled by the one or more user applications810 to request a route generation at block 1025. For example, generatinga request for route generation may include enabling the user to defineinitial constraints such as carrier objectives and/or constraints (e.g.,a desired start and/or end location, a start date and/or time, and/orthe like), information associated with the carrier, and/or the like. Therequest for route generation may be generated and/or received by the oneor more user applications 810 and transmitted to the inventory manager820 for processing. Route generation may further include generation ofone or more vehicle segments, calculation of an estimated route traveltime, an estimated cost of fuel for completing the generated route,and/or the like. The generated route and/or associated information maybe transmitted to the user in a report, an email, a text message, aseries of global positioning system (GPS) coordinates, and/or the like.

The inventory manager 820 may receive the request for route generationfrom the one or more user applications 810. Upon receipt of the requestfor route generation and at block 1035, the inventory manager 820 mayadd the carrier associated with the request for route generation to abatch manager. In some embodiments, the batch manager is a portion ofthe inventory manager 820 that is configured to coordinate aggregationof all vehicle records of vehicles that are available to be transportedby multiple carriers. For example, at block 1040, an inventory of allvehicle records of vehicles that have been verified and placed in theinventory manager 820 may be imported by the batch manager.

Next, the imported vehicle records of vehicles may be transmitted fromthe inventory manager 820 to the optimizer 830 for processing. Theoptimizer 830, upon receiving the imported vehicle records of availablevehicles may, at block 1045, identify one or more vehicle records ofvehicles and/or segments of vehicles that are available for transport bythe carrier using processes disclosed herein (e.g., an algorithm). Forexample, the optimizer 830 may identify one or more vehicle records ofvehicles and/or segments of vehicles that are available for transport bythe carrier based on the carrier objectives and/or carrier constraintsdefined by the user at blocks 1015 and/or 1030. Alternatively, theoptimizer 830 may receive from the inventory manager 820 a listingincluding one or more vehicles that are available for inclusion in oneor more optimized solution sets. Then, the optimizer 830 may, based oncomparing and/or matching information and/or attributes associated witheach available vehicle (e.g., information and/or attributes included inone or more vehicle records of the vehicles included in the listing ofavailable vehicles) to carrier preferences (e.g., carrier objectivesand/or carrier constraints) of a carrier, identify one or more vehiclesthat are eligible for inclusion in one or more optimized solution setsfor the carrier (e.g., the carrier associated with the user). Theoptimizer 830 may then analyze and/or compare all eligible vehicles toidentify one or more vehicles to be included an optimized solution set.For example, the optimizer 830 may determine one or more vehicles to beincluded in an optimized solution that minimizes a distance of anoverall route for the carrier, that maximizes profit of the carrier,that minimizes an amount of fuel expenses for the carrier, that avoidsparticular hazards such as weather and/or construction, that minimizes anumber of miles driven by the carrier loaded below a predeterminedcapacity, that minimizes a distance between one or more pick-ups and/ordeliveries, that minimizes a time required by a carrier to load and/orunload one or more vehicles during one or more pick-ups and/ordeliveries, that minimizes an amount of potential harm and/or damagewhen loading and/or unloading a carrier, and/or the like. In thismanner, the optimizer 830 may generate one or more optimized solutionsets using the identified one or more vehicle records of vehicles and/orsegments of vehicles that are available for transport by the carrier.Again, the one or more optimized solution sets may include one or morevehicles, vehicle segments, and/or routes for transporting the one ormore vehicles.

In some embodiments, each vehicle included in each of the one or moregenerated optimized solution sets is exclusive to the optimized solutionset in which the vehicle is included. As such, at block 1050, theoptimizer 830 and/or the inventory manager 830 may hold and/or removeeach vehicle record of a vehicle that has been included in an optimizedsolution set from a list and/or an inventory of vehicle records ofvehicles available to be transported by a carrier. In this manner, eachvehicle may only be assigned to, allocated to, and/or included in onesolution set presented to one carrier.

The optimizer 830 may transmit the one or more generated optimizedsolution sets to the inventory manager 820, which may update theinventory list and/or an inventory of vehicle records of vehiclesavailable to be transported by a carrier based on the vehicles includedin the one or more optimized solution sets. Further at block 1050, theone or more generated optimized solution sets may then be transmitted tothe user application for presentation to the user and/or user selection.

If the user rejects and/or does not wish to select one or more of theone or more generated optimized solution sets and/or if an optimizedsolution set is not selected for a predetermined period of time, such asat block 1055, the one or more user applications 810, the inventorymanager 820, and/or the optimizer 830 may release any exclusionary holdson vehicle records of vehicles included in unselected optimized solutionsets, and the vehicle records of vehicles included in unselectedoptimized solution sets may be reintroduced and/or re-included in theinventory of vehicle records of vehicles that are available fortransport by a carrier. Further, the user may be directed by the one ormore user applications 810 to input new and/or modify existing initialconstraints (e.g., carrier objectives and/or carrier constraints) atblock 1030. In other embodiments and at block 1060, the user may belogged out of the user application 810.

The user may accept and/or select an optimized solution set (e.g., asuggested route including one or more vehicle transportation segments)at block 1065 and therefore accepts responsibility for transporting thevehicles included in the selected optimized solution set. At blocks 1065and/or 1070, the user may further be enabled by the one or more userapplications 810 to adjust and/or modify elements on the one or moregenerated optimized solution sets. For example, the user may delete oneor more vehicles, route segments, and/or the like from an optimizedsolution set. In this manner, the user may further optimize theirvehicle transportation route. Alternatively, the user may accept and/orselect an optimized solution set without making any modifications to theoptimized solution set. Again, the one or more user applications 810,the inventory manager 820, and/or the optimizer 830 may release anyexclusionary holds on vehicle records of vehicles included in anoptimized solution set that is de-selected, removed, deleted, and/or thelike by the user, and the vehicle records of vehicles that were deletedfrom an optimized solution set may be reintroduced and/or re-included inthe inventory of vehicle records of vehicles that are available fortransport by a carrier.

Upon selection of an optimized solution set and at block 1075, theinventory manager 120 may assign each vehicle included in the selectedoptimized solution set to the carrier. In some embodiments, assigningeach vehicle included in the selected optimized solution set to thecarrier includes dispatching each vehicle included in the selectedoptimized solution set to the carrier. Assigning each vehicle includedin the selected optimized solution set to the carrier may furtherinclude assigning and/or correlating in the archival database 830information and/or attributes of each vehicle included in the selectedoptimized solution set to carrier objectives and/or carrier constraintsof the carrier and/or to information associated with the selectedoptimized solution set such as route information. Assigning each vehicleincluded in the selected optimized solution set to the carrier may alsoinclude generating a schedule and/or itinerary for the carrier detailinga route, carrier objectives and/or carrier constraints, informationand/or attributes associated with each vehicle included in the selectedoptimized solution set, and/or the like.

Additionally, a contractual agreement may be generated by the one ormore user applications 810, the inventory manager 820 in response toassigning each vehicle included in the selected optimized solution setto the carrier. In some embodiments, a user selection and/or acceptanceof an optimized solution set may automatically enter the user and/or thecarrier associated with the route generation request into a contractualagreement between the carrier and the shipper, the supplier, the buyer,the purchaser, the seller, and/or the like. The user may continue bylogging out of the one or more user applications at block 1060.

In some embodiments, the optimizer 830 may be configured to minimize anumber of carriers required to transport a set of vehicles whengenerating an optimized solution set. For example, the optimizer 830 maygenerate an optimized solution set based on attributes of one or morevehicles to be included in the optimized solution set, such as a vehicleweight, a vehicle size, a shipper fee, origin and/or destinationlocations, time windows for pick-up and/or delivery, and/or the like.Alternatively or additionally, the optimizer 830 may generate anoptimized solution set based on attributes of one or more carriers(e.g., carrier objectives and/or carrier constraints) to transport thevehicles included in the optimized solution set, such as load capacity(e.g., a carrier volume and/or a carrier weight), pre-existing loads onthe one or more carriers at various points during a route, a deliveryschedule, delivery costs, a currently location, a desired destinationlocation, and/or the like. In some embodiments, the optimizer 830 mayutilize heuristic modeling (e.g., parallel processing) to generate oneor more optimized solution sets simultaneously and/or in real time. Forexample, the optimizer 830 may generate a substantially large,representative number of possible optimized solution sets based on anavailable vehicle inventory, and then may intelligently search, sort,and/or the like through these representative solution sets to determineone or more optimized solution sets that maximize and/or minimize one ormore particular variables (e.g., profit, distance, cost, time, location,vehicle information and/or attributes, carrier constraints and/orcarrier objectives, and/or the like). The optimizer 830 may weight oneor more variables when searching so as to more quickly and efficientlyidentify one or more preferred optimized solution sets.

The optimizer 830 may generate and/or assign individual vehicle pick-upand/or deliver segments into a set of routes. Each route of the set ofroutes may define a sequence of stops corresponding to the componentsegments (e.g., pick-up and/or delivery of a vehicle included in anoptimized solution set of vehicles). In some embodiments, a route mayinclude a one-way transport or a round-trip transport of one or morevehicles. Alternatively, a route may include a planned round-triptransport route of a carrier, where one or more vehicles are transported(e.g., delivered and/or picked up) at various locations along theplanned carrier route. As routes and/or optimized solution sets arerejected and/or modified by the user, any vehicles and/or routes notselected by the user may be reintroduced and/or re-included in aninventory of vehicles available for transport. In this manner, theoptimizer 830 may re-optimize one or more optimized solution sets basedon modifications (e.g., removals, additions, and/or the like) ofvehicles and/or segments of routes from the one or more optimizedsolution sets to therefore generate one or more new optimized solutionsets which include an updated set of vehicles and/or route segments.

Additionally, some embodiments may include the optimizer 830 determininga route (e.g., a long route, a cross-country route, and/or the like) fortransporting one or more vehicles included in an optimized solution set.The optimizer 830 may then determine one or more subroutes that may beassigned to different carriers. Further, wholesale auction facilitiesmay be utilized as pick-up and/or delivery locations, staging locations,and/or the like. In this manner, segments of an optimized solution setmay include picking up and/or delivering one or more vehicles to anauction facility so that the one or more vehicles may be more easily(e.g., more profitably) transported by multiple carriers.

In some embodiments, generating the one or more optimized solution setsby the optimizer 830 may include calculating a price of each routeand/or a cost of transporting each vehicle included in the one or moreoptimized solution sets. In some embodiments, rate fluctuations based oncurrent conditions such as weather, seasonal migrations, and/or the likemay be included in pricing of each route and/or segment. Pricing oftransporting a vehicle and/or a set of vehicles may be determined basedat least in part on a vehicle price, a carrier type and/or inventory,weather, a driving record of the carrier, a driving history, a routehistory, a frequency of carrier travel along a particular route and/orto and/or from a particular location, preferred routes, insurance, areliability and/or review score of the carrier, and/or the like. In someembodiments, an estimated cost, an estimated margin, and/or a projectionof savings of selecting an optimized solution set may be determined andpresented to the carrier with each optimized solution set of vehiclesand/or route segments. For example, the optimizer 830 may determine aprice of each segment (e.g., a price associated with transporting eachvehicle) included in each optimized solution set and, based at leastpartially on the determined price of each segment, determine a totalprice of transporting all vehicles included in each optimized solutionset. Alternatively, other factors may be considered by the optimizer 830when determining a price, margin, and/or savings of each optimizedsolution set. Other factors may include weather information, fueleconomy, carrier constraints and/or carrier objectives, vehicleinformation and/or attributes, and/or the like. In some embodiments, theoptimizer 830 may utilize weights for various elements to determinepricing and/or generate one or more optimized solution sets.Additionally, the optimizer 830 may calculate pricing of transportingeach individual vehicle and/or pricing of transporting multiple vehiclesbundled in an optimized solution set.

In some embodiments, information (e.g., carrier objectives and/orcarrier constraints, information and/or attributes associated with avehicle, a vehicle record, and/or a vehicle transaction, weatherinformation, pricing information and/or market information, routeinformation and/or segment information, and/or the like) may be receivedin a continuous (e.g., real time) stream of data from a variety ofsources. For example, weather information may be received from aplurality of weather information sources, and then may be processed bythe system described herein to calculate an average temperature,calculate an estimated amount of precipitation, determine a level ofhazard associated with weather conditions, calculate an estimated priceand/or risk of transport based on weather conditions, and/or the like.Each piece of information may be weighted by the system described hereinso as to account for factors that are most critical to pricing and/orsafe transport of a vehicle. For example, in the winter, a segmentincluding a route through the Northeast United States during a projectedsnow storm may be priced higher so that the carrier is rewarded forincurring substantially more risk than transporting a vehicle along asegment in the sunny Southeast United States. In this manner, moreaccurate estimates of cost, price, time, and/or the like may becalculated and provided to the carrier, and each estimate and/orcalculation may be updated in real time as information is received andprocessed by the system.

Further, generating the one or more optimized solution sets by theoptimizer 830 may include determining a minimum number of carriersrequired to transport one or more vehicles to be included in a generatedoptimized solution set on which the generation is based. Generating theone or more optimized solution sets by the optimizer 830 may alsoinclude determining a maximum amount of revenue and/or efficiency for acarrier and/or a dispatcher on which the generation is based.

In some embodiments, the optimizer 830 may determine a route is optimalbased on geometries of loads (e.g., vehicles) to be transported by thecarrier and/or road hazards (e.g., weather conditions, road types,and/or the like). In other embodiments, the optimizer 830 may determinean optimal loading of vehicles onto a carrier based on vehicle size,shape, type, safety, convenience and/or speed of loading and/orunloading vehicles onto the carrier, and/or the like. For example, itmay be determined to be optimal to load a first vehicle onto a firstportion of a carrier and to load a second vehicle onto a second portionof the carrier. Alternatively or additionally, the optimizer 830 maydetermine an optimal route that minimizes a number of miles traveled bya carrier with a less-than-capacity load.

In some embodiments, it may be unprofitable for a carrier to transport afirst vehicle from its current location to its destination location.However, by optimally grouping and/or bundling the first vehicle withone or more other vehicles to be transported, transporting the firstvehicle may become profitable. In this manner, a potentiallyunprofitable vehicle transport segment (e.g., an outlier) may beincluded with one or more profitable vehicle transport segments in anoptimized solution set, and the optimized solution set may still beprofitable (e.g., an average of the profit associated with the outlierand the one or more profitable segments is greater than zero).

In some embodiments, multi-modal optimization architectures may beutilized by the optimizer 830. Utilizing multi-modal optimalarchitectures may include utilizing multiple modes of transportation foroptimally transporting one or vehicles. For example, the optimizer 830may determine that an optimal method of transporting a vehicle includesa first carrier (e.g., Truck 1) picking up the vehicle at a pick-uplocation and transporting the vehicle to a first train depot, where thevehicle may be loaded onto a railcar of a train for transport to asecond train depot. The train may transport the vehicle to the secondtrain depot, where a second carrier picks up the vehicle. The secondcarrier then may transport the vehicle to a destination location. Inthis manner, the optimizer 830 may utilize multiple transportation modeswhen determining an optimal route, solution set, and/or the like.

In some embodiments, any type of surface transportation (e.g., railcars,railways, trains, trams, sleds, and/or the like), naval and/or aquaticvehicles, aircraft, and/or the like may be utilized by the optimizer inmulti-modal optimization architectures. Utilizing different modes oftransportation may be more optimal than utilizing a singular mode oftransportation because each different mode of transportation may havedifferent schedules, travel times, routes, and/or the like that betterminimize and/or maximize one or more variables in the optimizationarchitectures. For example, utilizing a railcar to transport a vehiclemay be more efficient for a carrier to transport the vehicle becauseutilizing the railcar may minimize a number of miles traveled by thecarrier, or by avoiding delays caused by additional shorter vehicletransports that may be required to make the long-haul transporteconomical to the carrier. Additionally, carriers of different modes oftransportation may have different carrier configurations (e.g., arailcar is larger than a tractor trailer). Alternatively, if adestination location is on an island or other difficult-to-reach,isolated, and/or remote environment, utilizing multiple modes oftransportation may be necessary. In some embodiments, multi-modaloptimization architecture utilization may be a selectable optionpresented to the user (e.g., carrier) for selection.

FIG. 11 is a flow diagram illustrating details of an example method 1110for optimizing one or more carrier routes for picking up and/ordelivering multiple vehicles, according to one embodiment of thedisclosure. At block 1110, the method 1100 can include receiving one ormore carrier constraints of a carrier, wherein the carrier is configuredto transport one or more vehicles. At block 1120, the method 1100 caninclude receiving one or more vehicle attributes associated with one ormore vehicles available to be transported by the carrier. At block 1130,the method 1100 can include determining one or more optimal solutionsets based at least in part on the one or more carrier constraints andthe one or more vehicle attributes, wherein each optimal solution setcomprises at least one of the one or more vehicles available to betransported by the carrier. At block 1140, the method 1100 can includeproviding the one or more optimal solution sets to a user for selection.

Example embodiments of the disclosure provide a number of technicalfeatures, technical benefits, and technical effects. For example, inaccordance with example embodiments of the disclosure, multipleprocessor (e.g., GPU) threads may be utilized to determine, in parallel,solutions to an optimization problem within an assigned solution space,thereby reducing the processing time and processing load required toobtain a timely, high-quality solution to the optimization. In addition,in accordance with example embodiments of the disclosure, grouptheoretic techniques are used to model an optimization problem andfragment a solution space into partitions that can be processed byrespective processing threads, thereby providing an approach that allowselite solutions to be identified more efficiently, ultimately leading todetermination of a timely, high-quality solution with less processingtime. It should be appreciated that the above examples of technicalfeatures and/or technical effects of example embodiments of thedisclosure are merely illustrative and not exhaustive.

One or more illustrative embodiments of the disclosure have beendescribed above. The above-described embodiments are merely illustrativeof the scope of this disclosure and are not intended to be limiting inany way. Accordingly, variations, modifications, and equivalents ofembodiments disclosed herein are also within the scope of thisdisclosure. The above-described embodiments and additional and/oralternative embodiments of the disclosure will be described in detailhereinafter through reference to the accompanying drawings.

Illustrative Device Architecture

FIG. 12 is a schematic block diagram of an illustrative serverconfigured to execute GTTS processing in accordance with one or moreexample embodiments of the disclosure. In an illustrative configuration,the GTTS server 1200 may include one or more processors (processor(s))1202, one or more memory devices 1204 (generically referred to herein asmemory 1004), one or more input/output (“I/O”) interface(s) 1206, one ormore network interfaces 1208, and data storage 1210. The device 1200 mayfurther include one or more buses 1212 that functionally couple variouscomponents of the device 1200. These various components will bedescribed in more detail hereinafter.

The bus(es) 1212 may include at least one of a system bus, a memory bus,an address bus, or a message bus, and may permit exchange of information(e.g., data (including computer-executable code), signaling, etc.)between various components of the device 1200. The bus(es) 1212 mayinclude, without limitation, a memory bus or a memory controller, aperipheral bus, an accelerated graphics port, and so forth. The bus(es)1212 may be associated with any suitable bus architecture including,without limitation, an Industry Standard Architecture (ISA), a MicroChannel Architecture (MCA), an Enhanced ISA (EISA), a Video ElectronicsStandards Association (VESA) architecture, an Accelerated Graphics Port(AGP) architecture, a Peripheral Component Interconnects (PCI)architecture, a PCI-Express architecture, a Personal Computer MemoryCard International Association (PCMCIA) architecture, a Universal SerialBus (USB) architecture, and so forth.

The memory 1204 of the device 1200 may include volatile memory (memorythat maintains its state when supplied with power) such as random accessmemory (RAM) and/or non-volatile memory (memory that maintains its stateeven when not supplied with power) such as read-only memory (ROM), flashmemory, ferroelectric RAM (FRAM), and so forth. In certain exampleembodiments, volatile memory may enable faster read/write access thannon-volatile memory. However, in certain other example embodiments,certain types of non-volatile memory (e.g., FRAM) may enable fasterread/write access than certain types of volatile memory.

In various implementations, the memory 1204 may include multipledifferent types of memory such as various types of static random accessmemory (SRAM), various types of dynamic random access memory (DRAM),various types of unalterable ROM, and/or writeable variants of ROM suchas electrically erasable programmable read-only memory (EEPROM), flashmemory, and so forth. The memory 1204 may include main memory as well asvarious forms of cache memory such as instruction cache(s), datacache(s), translation lookaside buffer(s) (TLBs), and so forth. Further,cache memory such as a data cache may be a multi-level cache organizedas a hierarchy of one or more cache levels (L1, L2, etc.).

The data storage 1210 may include removable storage and/or non-removablestorage including, but not limited to, magnetic storage, optical diskstorage, solid-state storage, and/or tape storage. The data storage 1210may provide non-volatile storage of computer-executable instructions andother data. The memory 1204 and the data storage 1210, removable and/ornon-removable, are examples of computer-readable storage media (CRSM) asthat term is used herein.

The data storage 1210 may store computer-executable code, instructions,or the like that may be loadable into the memory 1204 and executable bythe processor(s) 1202 to cause the processor(s) 1202 to perform orinitiate various operations. The data storage 1214 may additionallystore data that may be copied to memory 1204 for use by the processor(s)1202 during the execution of the computer-executable instructions.Moreover, output data generated as a result of execution of thecomputer-executable instructions by the processor(s) 1202 may be storedinitially in memory 1204, and may ultimately be copied to data storage1210 for non-volatile storage.

More specifically, the data storage 1210 may store one or more operatingsystems (O/S) 1214; one or more database management systems (DBMS) 1216;and one or more program modules, applications, or the like such as, forexample, one or more solution space partitioning modules 1218 and one ormore GTTS processing modules 1220. The GTTS processing modules 1220 mayfurther include one or more sub-modules such as, for example, one ormore STM modules 1222, one or more intensification modules 1224, and oneor more diversification modules 1226.

The solution space partitioning module(s) 1218 may includecomputer-executable instructions, code, or the like that when executedby one or more of the processor(s) 1202 causes operations to beperformed for fragmenting a solution space to generate solution spacepartitions that can be processed by the GTTS processing module(s) 1220.In certain example embodiments, the GTTS processing module(s) 1220 mayinclude computer-executable instructions, code, or the like that areexecuted on executed on each GPU thread 128(1)-128(N) to cause each GPUthread to explore a respective solution space partition for elitesolutions to an optimization problem. The STM module(s) 1222 may includecomputer-executable instructions, code, or the like that when executedby one or more of the processor(s) 1202 causes operations to beperformed for executing an STM phase of tabu search. The STM phase mayinclude exploration of a diversification cell (e.g., a solution spacefragment) to determine elite solution(s). The intensification module(s)1224 may include computer-executable instructions, code, or the likethat when executed by one or more of the processor(s) 1202 may causeoperations to be performed for executing an intensification phase oftabu search. For example, when an STM phase fails to produce anyadditional elite solution, the GTTS processing module(s) 1218 may returnto the most elite solution determined thus far and may utilize theintensification module(s) 1224 to initiate an intensification phase inconnection with the most elite solution. For example, theintensification phase may include initiating a new STM phase inconnection with the most elite solution. The diversification module(s)1226 may include computer-executable instructions, code, or the likethat when executed by one or more of the processor(s) 1202 causesoperations to be performed for diversifying GTTS processing to a newdiversification cell.

The data storage 1210 may further store any of variety of other types ofmodules. Further, any program modules stored in the data storage 1210may include one or more sub-modules. Further, any data stored in thedata storage 1210 may be loaded into the memory 1204 for use by theprocessor(s) 1202 in executing computer-executable code. In addition,any data potentially stored in one or more datastores may be accessedvia the DBMS 1216 and loaded in the memory 1204 for use by theprocessor(s) 1202 in executing computer-executable code.

The processor(s) 1202 may be configured to access the memory 1204 andexecute computer-executable instructions loaded therein. For example,the processor(s) 1202 may be configured to execute computer-executableinstructions of the various program modules of the server 1200 to causeor facilitate various operations to be performed in accordance with oneor more embodiments of the disclosure. The processor(s) 1202 may includeany suitable processing unit capable of accepting data as input,processing the input data in accordance with stored computer-executableinstructions, and generating output data. The processor(s) 1202 mayinclude any type of suitable processing unit including, but not limitedto, a central processing unit (e.g., CPU 102), a graphical processingunit (e.g., GPU 104), a microprocessor, a Reduced Instruction SetComputer (RISC) microprocessor, a Complex Instruction Set Computer(CISC) microprocessor, a microcontroller, an Application SpecificIntegrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), aSystem-on-a-Chip (SoC), a digital signal processor (DSP), and so forth.Further, the processor(s) 1202 may have any suitable microarchitecturedesign that includes any number of constituent components such as, forexample, registers, multiplexers, arithmetic logic units, cachecontrollers for controlling read/write operations to cache memory,branch predictors, or the like. The microarchitecture design of theprocessor(s) 1202 may be capable of supporting any of a variety ofinstruction sets.

Referring now to other illustrative components depicted as being storedin the data storage 1210, the O/S 1214 may be loaded from the datastorage 1210 into the memory 1204 and may provide an interface betweenother application software executing on the server 1200 and hardwareresources of the server 1200. More specifically, the O/S 1214 mayinclude a set of computer-executable instructions for managing hardwareresources of the server 1200 and for providing common services to otherapplication programs (e.g., managing memory allocation among variousapplication programs). The O/S 1214 may include any operating system nowknown or which may be developed in the future including, but not limitedto, any server operating system, any mainframe operating system, or anyother proprietary or non-proprietary operating system.

The DBMS 1216 may be loaded into the memory 1204 and may supportfunctionality for accessing, retrieving, storing, and/or manipulatingdata stored in the memory 1204, data stored in the data storage 1210,and/or data stored in one or more datastores (e.g., the archivaldatastore(s) 120). The DBMS 1216 may use any of a variety of databasemodels (e.g., relational model, object model, etc.) and may support anyof a variety of query languages. The DBMS 1216 may access datarepresented in one or more data schemas and stored in any suitable datarepository including, but not limited to, databases (e.g., relational,object-oriented, etc.), file systems, flat files, distributed datastoresin which data is stored on more than one node of a computer network,peer-to-peer network datastores, or the like. In those exampleembodiments in which the server 1200 is a mobile device, the DBMS 1216may be any suitable light-weight DBMS optimized for performance on amobile device. It should be appreciated that “data,” as that term isused herein, may include computer-executable instructions, code, or thelike.

Referring now to other illustrative components of the server 1200, theone or more input/output (I/O) interfaces 1206 may facilitate thereceipt of input information by the device 1000 from one or more I/Odevices as well as the output of information from the server 1200 to theone or more I/O devices. The I/O devices may include any of a variety ofcomponents such as a display or display screen having a touch surface ortouchscreen; an audio output device for producing sound, such as aspeaker; an audio capture device, such as a microphone; an image and/orvideo capture device, such as a camera; a haptic unit; and so forth. Anyof these components may be integrated into the server 1200 or may beseparate. The I/O devices may further include, for example, any numberof peripheral devices such as data storage devices, printing devices,and so forth.

The I/O interface(s) 1206 may also include an interface for an externalperipheral device connection such as universal serial bus (USB),FireWire, Thunderbolt, Ethernet port or other connection protocol thatmay connect to one or more networks. The I/O interface(s) 1206 may alsoinclude a connection to one or more antennas to connect to one or morenetworks via a wireless local area network (WLAN) (such as Wi-Fi) radio,Bluetooth, and/or a wireless network radio, such as a radio capable ofcommunication with a wireless communication network such as a Long TermEvolution (LTE) network, WiMAX network, 3G network, etc.

The server 1200 may further include one or more network interfaces 1208via which the server 1200 may communicate with any of a variety of othersystems, platforms, networks, devices, and so forth. Such communicationmay occur via one or more networks including, but are not limited to,any one or more different types of communications networks such as, forexample, cable networks, public networks (e.g., the Internet), privatenetworks (e.g., frame-relay networks), wireless networks, cellularnetworks, telephone networks (e.g., a public switched telephonenetwork), or any other suitable private or public packet-switched orcircuit-switched networks. Further, such network(s) may have anysuitable communication range associated therewith and may include, forexample, global networks (e.g., the Internet), metropolitan areanetworks (MANs), wide area networks (WANs), local area networks (LANs),or personal area networks (PANs). In addition, such network(s) mayinclude communication links and associated networking devices (e.g.,link-layer switches, routers, etc.) for transmitting network trafficover any suitable type of medium including, but not limited to, coaxialcable, twisted-pair wire (e.g., twisted-pair copper wire), opticalfiber, a hybrid fiber-coaxial (HFC) medium, a microwave medium, a radiofrequency communication medium, a satellite communication medium, or anycombination thereof.

It should be appreciated that the program modules, applications,computer-executable instructions, code, or the like depicted in FIG. 12as being stored in the data storage 1210 are merely illustrative and notexhaustive and that processing described as being supported by anyparticular module may alternatively be distributed across multiplemodules or performed by a different module. In addition, various programmodule(s), script(s), plug-in(s), Application Programming Interface(s)(API(s)), or any other suitable computer-executable code hosted locallyon the server 1200, and/or hosted on other computing device(s)accessible via one or more networks, may be provided to supportfunctionality provided by the program modules, applications, orcomputer-executable code depicted in FIG. 12 and/or additional oralternate functionality. Further, functionality may be modularizeddifferently such that processing described as being supportedcollectively by the collection of program modules depicted in FIG. 12may be performed by a fewer or greater number of modules, orfunctionality described as being supported by any particular module maybe supported, at least in part, by another module. In addition, programmodules that support the functionality described herein may form part ofone or more applications executable across any number of systems ordevices in accordance with any suitable computing model such as, forexample, a client-server model, a peer-to-peer model, and so forth. Inaddition, any of the functionality described as being supported by anyof the program modules depicted in FIG. 12 may be implemented, at leastpartially, in hardware and/or firmware across any number of devices.

It should further be appreciated that the server 1200 may includealternate and/or additional hardware, software, or firmware componentsbeyond those described or depicted without departing from the scope ofthe disclosure. More particularly, it should be appreciated thatsoftware, firmware, or hardware components depicted as forming part ofthe server 1200 are merely illustrative and that some components may notbe present or additional components may be provided in variousembodiments. While various illustrative program modules have beendepicted and described as software modules stored in data storage 1210,it should be appreciated that functionality described as being supportedby the program modules may be enabled by any combination of hardware,software, and/or firmware. It should further be appreciated that each ofthe above-mentioned modules may, in various embodiments, represent alogical partitioning of supported functionality. This logicalpartitioning is depicted for ease of explanation of the functionalityand may not be representative of the structure of software, hardware,and/or firmware for implementing the functionality. Accordingly, itshould be appreciated that functionality described as being provided bya particular module may, in various embodiments, be provided at least inpart by one or more other modules. Further, one or more depicted modulesmay not be present in certain embodiments, while in other embodiments,additional modules not depicted may be present and may support at leasta portion of the described functionality and/or additionalfunctionality. Moreover, while certain modules may be depicted anddescribed as sub-modules of another module, in certain embodiments, suchmodules may be provided as independent modules or as sub-modules ofother modules.

One or more operations of the methods 600-700 may be performed by one ormore components of the server 1200, or more specifically, by one or moreone or more program modules executing on such a server 1200. It shouldbe appreciated, however, that any of the operations of methods 600-700may be performed, at least in part, in a distributed manner by one ormore other devices or systems, or more specifically, by one or moreprogram modules, applications, or the like executing on such devices. Inaddition, it should be appreciated that processing performed in responseto execution of computer-executable instructions provided as part of anapplication, program module, or the like may be interchangeablydescribed herein as being performed by the application or the programmodule itself or by a device on which the application, program module,or the like is executing. While the operations of any of the methods600-700 may be described in the context of the illustrative server 1200,it should be appreciated that such operations may be implemented inconnection with numerous other system configurations.

The operations described and depicted in the illustrative methods ofFIG. 6-7 may be carried out or performed in any suitable order asdesired in various example embodiments of the disclosure. Additionally,in certain example embodiments, at least a portion of the operations maybe carried out in parallel. Furthermore, in certain example embodiments,less, more, or different operations than those depicted in FIGS. 6-7 maybe performed.

Although specific embodiments of the disclosure have been described, oneof ordinary skill in the art will recognize that numerous othermodifications and alternative embodiments are within the scope of thedisclosure. For example, any of the functionality and/or processingcapabilities described with respect to a particular device or componentmay be performed by any other device or component. Further, whilevarious illustrative implementations and architectures have beendescribed in accordance with embodiments of the disclosure, one ofordinary skill in the art will appreciate that numerous othermodifications to the illustrative implementations and architecturesdescribed herein are also within the scope of this disclosure.

Certain aspects of the disclosure are described above with reference toblock and flow diagrams of systems, methods, apparatuses, and/orcomputer program products according to example embodiments. It will beunderstood that one or more blocks of the block diagrams and flowdiagrams, and combinations of blocks in the block diagrams and the flowdiagrams, respectively, may be implemented by execution ofcomputer-executable program instructions. Likewise, some blocks of theblock diagrams and flow diagrams may not necessarily need to beperformed in the order presented, or may not necessarily need to beperformed at all, according to some embodiments. Further, additionalcomponents and/or operations beyond those depicted in blocks of theblock and/or flow diagrams may be present in certain embodiments.

Accordingly, blocks of the block diagrams and flow diagrams supportcombinations of means for performing the specified functions,combinations of elements or steps for performing the specifiedfunctions, and program instruction means for performing the specifiedfunctions. It will also be understood that each block of the blockdiagrams and flow diagrams, and combinations of blocks in the blockdiagrams and flow diagrams, may be implemented by special-purpose,hardware-based computer systems that perform the specified functions,elements or steps, or combinations of special-purpose hardware andcomputer instructions.

Program modules, applications, or the like disclosed herein may includeone or more software components including, for example, softwareobjects, methods, data structures, or the like. Each such softwarecomponent may include computer-executable instructions that, responsiveto execution, cause at least a portion of the functionality describedherein (e.g., one or more operations of the illustrative methodsdescribed herein) to be performed.

A software component may be coded in any of a variety of programminglanguages. An illustrative programming language may be a lower-levelprogramming language such as an assembly language associated with aparticular hardware architecture and/or operating system platform. Asoftware component comprising assembly language instructions may requireconversion into executable machine code by an assembler prior toexecution by the hardware architecture and/or platform.

Another example programming language may be a higher-level programminglanguage that may be portable across multiple architectures. A softwarecomponent comprising higher-level programming language instructions mayrequire conversion to an intermediate representation by an interpreteror a compiler prior to execution.

Other examples of programming languages include, but are not limited to,a macro language, a shell or command language, a job control language, ascript language, a database query or search language, or a reportwriting language. In one or more example embodiments, a softwarecomponent comprising instructions in one of the foregoing examples ofprogramming languages may be executed directly by an operating system orother software component without having to be first transformed intoanother form.

A software component may be stored as a file or other data storageconstruct. Software components of a similar type or functionally relatedmay be stored together such as, for example, in a particular directory,folder, or library. Software components may be static (e.g.,pre-established or fixed) or dynamic (e.g., created or modified at thetime of execution).

Software components may invoke or be invoked by other softwarecomponents through any of a wide variety of mechanisms. Invoked orinvoking software components may comprise other custom-developedapplication software, operating system functionality (e.g., devicedrivers, data storage (e.g., file management) routines, other commonroutines and services, etc.), or third-party software components (e.g.,middleware, encryption, or other security software, database managementsoftware, file transfer or other network communication software,mathematical or statistical software, image processing software, andformat translation software).

Software components associated with a particular solution or system mayreside and be executed on a single platform or may be distributed acrossmultiple platforms. The multiple platforms may be associated with morethan one hardware vendor, underlying chip technology, or operatingsystem. Furthermore, software components associated with a particularsolution or system may be initially written in one or more programminglanguages, but may invoke software components written in anotherprogramming language.

Computer-executable program instructions may be loaded onto aspecial-purpose computer or other particular machine, a processor, orother programmable data processing apparatus to produce a particularmachine, such that execution of the instructions on the computer,processor, or other programmable data processing apparatus causes one ormore functions or operations specified in the flow diagrams to beperformed. These computer program instructions may also be stored in acomputer-readable storage medium (CRSM) that upon execution may direct acomputer or other programmable data processing apparatus to function ina particular manner, such that the instructions stored in thecomputer-readable storage medium produce an article of manufactureincluding instruction means that implement one or more functions oroperations specified in the flow diagrams. The computer programinstructions may also be loaded onto a computer or other programmabledata processing apparatus to cause a series of operational elements orsteps to be performed on the computer or other programmable apparatus toproduce a computer-implemented process.

Additional types of CRSM that may be present in any of the devicesdescribed herein may include, but are not limited to, programmablerandom access memory (PRAM), SRAM, DRAM, RAM, ROM, electrically erasableprogrammable read-only memory (EEPROM), flash memory or other memorytechnology, compact disc read-only memory (CD-ROM), digital versatiledisc (DVD) or other optical storage, magnetic cassettes, magnetic tape,magnetic disk storage or other magnetic storage devices, or any othermedium which can be used to store the information and which can beaccessed. Combinations of any of the above are also included within thescope of CRSM. Alternatively, computer-readable communication media(CRCM) may include computer-readable instructions, program modules, orother data transmitted within a data signal, such as a carrier wave, orother transmission. However, as used herein, CRSM does not include CRCM.

Although embodiments have been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the disclosure is not necessarily limited to the specific featuresor acts described. Rather, the specific features and acts are disclosedas illustrative forms of implementing the embodiments. Conditionallanguage, such as, among others, “can,” “could,” “might,” or “may,”unless specifically stated otherwise, or otherwise understood within thecontext as used, is generally intended to convey that certainembodiments could include, while other embodiments do not include,certain features, elements, and/or steps. Thus, such conditionallanguage is not generally intended to imply that features, elements,and/or steps are in any way required for one or more embodiments or thatone or more embodiments necessarily include logic for deciding, with orwithout user input or prompting, whether these features, elements,and/or steps are included or are to be performed in any particularembodiment.

That which is claimed is:
 1. A system, comprising: a central processingunit (CPU); a graphical processing unit (GPU) comprising a plurality ofarithmetic logic units (ALUs); at least one memory storingcomputer-executable instructions; and one or more buses that operativelycouple the CPU, the GPU, and the at least one memory, wherein the CPU isconfigured to access the at least one memory via at least one bus of theone or more buses and execute the computer-executable instructions to:receive one or more vehicle attributes associated with one or morevehicles available to be transported by one or more carriers; determinea solution space for an optimization problem associated withtransportation of the one or more vehicles, wherein at least a portionof the solution space is represented by a first matrix; determine, basedon Group Theoretic Tabu Search (GTTS) processing, an initial solution tothe optimization problem within a first cell of the solution space andan initial fragmentation of the solution space; fragment the initialfragmentation into a proper subgroup of the initial fragmentation,wherein the proper subgroup comprises into a plurality of cells, whereineach cell comprises a respective disjoint subset of the solution space,wherein the plurality of cells are determined using negative arcscorresponding to negative entries in a second matrix, wherein the secondmatrix is determined by subtracting the initial solution from one ormore rows of the first matrix; cause the GPU to launch a respective GPUthread to perform GTTS processing on a corresponding cell of theplurality of cells, wherein each respective GPU thread utilizes acorresponding ALU of the plurality of ALUs to process the correspondingcell to determine a respective solution to the optimization problem;determine one or more optimal solution sets; and send the one or moreoptimal solution sets to a user device for selection via an onlinemarketplace over a network.
 2. The system of claim 1, wherein the CPU isfurther configured to execute the computer-executable instructions to:launch a plurality of kernels on the at least one memory, wherein eachkernel is associated with a corresponding respective GPU thread.
 3. Thesystem of claim 1, wherein the plurality of cells is a first pluralityof cells, and wherein the CPU is further configured to execute thecomputer-executable instructions to: fragment the solution space into asecond plurality of cells that is different from the first plurality ofcells based at least in part on the respective solution to theoptimization problem determined by each respective GPU thread.
 4. Thesystem of claim 1, wherein the CPU is further configured to execute thecomputer-executable instructions to: receive one or more carrierconstraints of a carrier, wherein the carrier is configured to transportone or more vehicles; receive one or more vehicle attributes associatedwith one or more vehicles available to be transported by the carrier;determine one or more optimal solution sets based at least in part onthe one or more carrier constraints and the one or more vehicleattributes based at least in part on the processing of the plurality ofcells; and provide the one or more optimal solution sets to a userdevice.
 5. The system of claim 4, wherein the CPU is further configuredto execute the computer-executable instructions to: receive from a userdevice a modification to the optimal solution, wherein modificationcomprises at least one of adding, deleting, accepting, trading,swapping, rejecting, and modifying at least one of the one or morevehicles comprised in the one or more optimal solution sets.
 6. Thesystem of claim 4, wherein each of the one or more vehicles available tobe transported by the carrier is associated with an optimized routesegment for transporting each respective vehicle from a pick-up locationto a delivery location.
 7. The system of claim 4, wherein the CPU isfurther configured to execute the computer-executable instructions to:assign a selected optimal solution set to the carrier; generate aschedule for the carrier to transport each vehicle included in theselected optimal solution set; and provide instructions for dispatchingeach vehicle included in the selected optimal solution set to betransported by the carrier according to the schedule.
 8. The system ofclaim 4, wherein the one or more optimal solution sets are provided to auser device for selection via an online marketplace listing over awireless network.
 9. The system of claim 1, wherein causing the GPU tolaunch a respective GPU thread to perform GTTS processing on acorresponding cell of the plurality of cells further comprises using across-cell transversal, wherein the cross-cell transversal comprises:perform GTTS processing on a first cell of the plurality of cells;perform GTTS processing on a second cell of the plurality of cells;index the first cell and the second cell; determine that a transversalvalue is less than a threshold value; and store, based on thedetermination that the transversal value is less than the thresholdvalue, data indicating the GTTS processing of the first cell and thesecond cell, wherein the data provides an indication that the first celland second cell have been processed to prevent cycling of the first celland second cell in subsequent GTTS processing.
 10. A non-transitorycomputer-readable medium storing computer-executable instructions, thatwhen executed by at least one processor, cause the at least oneprocessor to: receive one or more vehicle attributes associated with oneor more vehicles available to be transported by one or more carriers;determine a solution space for an optimization problem associated withtransportation of the one or more vehicles, wherein at least a portionof the solution space is represented by a first matrix; determine, basedon Group Theoretic Tabu Search (GTTS) processing, an initial solution tothe optimization problem within a first cell and an initialfragmentation of the solution space; fragment the initial fragmentationinto a proper subgroup of the initial fragmentation, wherein the propersubgroup comprises a plurality of cells, wherein each cell comprises arespective disjoint subset of the solution space, wherein the pluralityof cells are determined using negative arcs corresponding to negativeentries in a second matrix, wherein the second matrix is determined bysubtracting the initial solution from one or more rows of the firstmatrix; cause a GPU to launch a respective GPU thread to perform GTTSprocessing on a corresponding cell of the plurality of cells, whereineach respective GPU thread utilizes a corresponding arithmetic logicunit (ALU) of a plurality of ALUs of the GPU to process thecorresponding cell to determine a respective solution to theoptimization problem; determine one or more optimal solution sets; andsend the one or more optimal solution sets to a user device forselection via an online marketplace over a network.
 11. Thenon-transitory computer-readable medium of claim 10, whereincomputer-executable instructions further cause the at least oneprocessor to: launch a plurality of kernels, wherein each kernel isassociated with a corresponding respective GPU thread.
 12. Thenon-transitory computer-readable medium of claim 10, wherein theplurality of cells is a first plurality of cells, and whereincomputer-executable instructions further cause the at least oneprocessor to: fragment the solution space into a second plurality ofcells that is different from the first plurality of cells based at leastin part on the respective solution to the optimization problemdetermined by each respective GPU thread.
 13. The non-transitorycomputer-readable medium of claim 10, wherein computer-executableinstructions further cause the at least one processor to: receive one ormore carrier constraints of a carrier, wherein the carrier is configuredto transport one or more vehicles; determine one or more optimalsolution sets based at least in part on the one or more carrierconstraints and the one or more vehicle attributes based at least inpart on the processing of the plurality of cells; and provide the one ormore optimal solution sets to a user device.
 14. The non-transitorycomputer-readable medium of claim 13, wherein computer-executableinstructions further cause the at least one processor to: receive from auser device a modification to the optimal solution, wherein modificationcomprises at least one of adding, deleting, accepting, trading,swapping, rejecting, and modifying at least one of the one or morevehicles comprised in the one or more optimal solution sets.
 15. Thenon-transitory computer-readable medium of claim 13, wherein each of theone or more vehicles available to be transported by the carrier isassociated with an optimized route segment for transporting eachrespective vehicle from a pick-up location to a delivery location. 16.The non-transitory computer-readable medium of claim 13, whereincomputer-executable instructions further cause the at least oneprocessor to: assign a selected optimal solution set to the carrier;generate a schedule for the carrier to transport each vehicle includedin the selected optimal solution set; and provide instructions fordispatching each vehicle included in the selected optimal solution setto be transported by the carrier according to the schedule.
 17. A methodcomprising: receiving one or more vehicle attributes associated with oneor more vehicles available to be transported by one or more carriers;determining a solution space for an optimization problem associated withtransportation of the one or more vehicles, wherein at least a portionof the solution space is represented by a first matrix; determining,based on Group Theoretic Tabu Search (GTTS) processing, an initialsolution to the optimization problem within a first cell and an initialfragmentation of the solution space; fragmenting the initialfragmentation into a proper subgroup of the initial fragmentation,wherein the proper subgroup comprises a plurality of cells, wherein eachcell comprises a respective disjoint subset of the solution space,wherein the plurality of cells are determined using negative arcscorresponding to negative entries in a second matrix, wherein the secondmatrix is determined by subtracting the initial solution from one ormore rows of the first matrix; causing a GPU to launch a respective GPUthread to perform GTTS processing on a corresponding cell of theplurality of cells, wherein each respective GPU thread utilizes acorresponding arithmetic logic unit (ALU) of a plurality of ALUs of theGPU to process the corresponding cell to determine a respective solutionto the optimization problem; determining one or more optimal solutionsets; and sending the one or more optimal solution sets to a user devicefor selection via an online marketplace over a network.